A cold sunny day in December. Bill Nighy is sitting in the back of a black SUV as it heads south on Park Avenue towards the Morgan Library in Midtown, New York. He is dressed in a long black overcoat with a cashmere scarf tied around his neck and chunky black Eric Morecambe glasses. We are on our way to an exhibition, Bob Dylan's American Journey, 1956-1966. Nighy has a fanatical devotion to Dylan. Every night, as he climbs the stairs before taking the stage on Broadway in The Vertical Hour, he has a ritual. He says under his breath: "I can't believe I'm walking on to this f***ing tune." The song is Simple Twist of Fate and it's one of his favourites. Sam Mendes, the director of the play, chose it.

Nighy first heard Blood on the Tracks in Liverpool. It was 1975 and he was part of the Everyman Theatre company with Julie Walters and Pete Postlethwaite. He bought the album the day it came out, went into his room and stayed there for two weeks listening. When it finished, he would put the needle right back on. "I couldn't get over it. Couldn't recover from it. It's thrilling."

Nighy is 57 and has a nervous energy. Is he tense? Is he relaxed? He seems to be both at the same time. It's an endearing social awkwardness. An eagerness to want to say the right thing. He's been called "the thinking woman's crumpet", but he shrugs, and says he always thought of himself more as "the drinking woman's crumpet".

His allure is not premeditated - he doesn't strike an attitude. And despite his efforts to be accessible, there is something distinctly unavailable about him too.

He bought the first Dylan album on a whim. He had read a tiny article in the newspaper that said: "Genius folk singer Bob Dylan left London today after a successful engagement at the 100 Club." Nighy recites this sentence from a 30-year-old article as though it were part of the scriptures. "I don't think I'd ever seen the word 'genius' written down before. And it was also largely that it came before the words 'folk singer'."

He explains that he is drawn to how Dylan tells a story, in part because the expression isn't compromised. He tells it like you'd say it. And yet it's singing. The same could be said for Nighy's acting. Having seen him the night before in the play, he takes purposely stiff dialogue and slackens it, loosens it - makes it seem natural. _The play has had mixed reviews, but Nighy's performance has been unanimously embraced by the critics. He stars alongside Julianne Moore, and The New York Times wrote: "Mr Nighy, to put it bluntly, mops the floor with Ms Moore. You could even say, that with his irresistibly mannered performance, he mops the floor with Mr Hare's play. Under the circumstances this can only be counted as a blessing."

The wry understatement that charms audiences on stage is present off stage too. The restless bouncing, twitching , his wiry, nimble limbs and agile, lanky frame - all of it works to his advantage. But even though the mannerisms might be practised, none of it's forced.

To really understand Bill Nighy, you need to know about Bob Dylan. He is, Nighy says definitively, the most important artist in his life. There isn't a day that goes by where he doesn't listen to him. "If I'm in trouble, I go to Bob Dylan. And if I'm feeling really good, I go to Bob Dylan. I don't know where I'd be without him, really. I'm never tired of listening to any of it."

And what if Diana Quick, whom he refers to as his wife because the word "partner" is weird after 25 years, was not a fan of Bob Dylan? Would that have been a deal-breaker? "No, no," he says quite seriously.

"I understand that the world is divided. It started with my mother - 'He's a very good songwriter, but he should leave others to sing.' I have to live in the world with these people. So I have to let it go."

He's given up converting. It's like converting Americans to football, he says, so sparking a discussion about what he does when he's not on stage. "I find the Fox soccer channel and I watch the English Premiership. I love all of it."

Crystal Palace are his team, and he also adores watching David Beckham. Nighy laments the loss of Beckham as England captain. "I found it mysterious that he should be singled out, presumably because of a disappointing campaign, when I thought - unless I'm going crazy - that he had done as much as anyone involved to get us there. I think he's a wonderful athlete. A brilliant footballer. An exemplary man and a great ambassador for England and for the game. He's given me so much pleasure, David Beckham. I admire him tremendously."

Because of holiday shoppers, traffic is slow. Nighy adores New York and is happy to be working at Christmas. He doesn't like what he refers to as "scheduled fun". He's not prone to depression but spends a lot of time alone.

We arrive at the museum and he walks briskly as we search for the entrance. It's 4 o'clock in the afternoon and the exhibit will be closing soon. Just as we enter the gallery, a chatty couple approaches the diffident Englishman.

They had seen the play the night before and thank him for his performance. Nighy is gracious, looks relieved, and thanks them. It's all very polite. Then the husband asks Nighy if he ever read the reviews for Love Actually. He says no. "Good. Don't!" The man snorts, a typical New Yorker. Nighy looks a little unsettled and we move on.

Because serious recognition came late in his career, he can enjoy the attention he gets. You can tell he appreciates his success. "Nothing much has changed. There's not a lot to handle. The work has changed - and that's good. What's happened is, it's made me much more useful and castable and I have choices now that I'm very, very grateful for. And it's astonishing this late in the game.

"But I wasn't waiting for it to happen. It's an uncertain life and nobody's progress is assured. Like every English actor, the major concern if you have a family is to get through the month - get through the year. I've always been lucky. I've always had a gig."

Earlier in the day, when we first met over tea, he talked of how acting, in the beginning, was always a way out of doing other stuff. "I wasn't drawn to act," he said, brushing his hand over the crown of his head. "I thought, 'In a minute I'll give it up and get round to what I'm supposed to be doing' - but I never worked that out, and I'm a procrastinator of the highest order. So they kept giving me jobs and I went from job to job.

"They used to say, 'You must be prepared for long periods of unemployment,' and whenever anyone said that, I'd quietly exult because this was what I had in mind. The idea that you could legitimately loaf was glamorous for me."

He was good at putting things off and made it up as he went along. In a way, he still does.

We had been at the hotel having tea for a little over an hour when the noise in the bar area had become significantly louder. "Should we move?" Nighy asked. I suggested we go for a walk. It was the afternoon and he had a few hours before his performance that evening, so maybe there was something else he'd rather do? A friend of his had mentioned the Dylan exhibit. He had a waiting car and a driver, and so we were off.

Bill Nighy was born in 1949 and the reality of life hit him in his late teens. "That's when I found out that apparently you were required to get _up every day and go somewhere you didn't like."

He was an average student until he started worrying about things like his hair - and girls. "I was doing very well until I was 14 years old, and then I collapsed."

He left school shortly before he turned 16, and had no further education. He ran away, wanting to get to Iran ("which shows you how old I am, because it was then the Persian Gulf"), but only got as far as the south of France. Out of ideas and out of cash, he went to the British consulate somewhere near Marseilles and his father had to pay £25 to get him back.

"I was in serious trouble. I went back home, went to school over the summer, flunked, didn't make it through the exams, and then went to youth employment with Mum."

When asked by a man at the employment centre what he wanted to be, he wasn't trying to be funny when he said: "I want to be an author."

"That was to alert him to the fact. I didn't expect him to get me a job authoring anywhere."

At school, writing was the only thing he was complimented on, and his dreams to be a writer were founded on the thrill he got from reading. He was filled with self-doubt and would retreat into the world of books, where he felt safest. Music came later.

Authors like Ford Madox Ford and Hemingway inspired him, but the writing didn't happen. The youth-employment agency found him a job as a messenger boy for The Field magazine in London. Nighy delivered the magazines to hotels in black cabs; it seemed exciting.

Where he came from, becoming an actor was never a career option. He was born in Caterham, Surrey - his father managed a garage and his mum was a psychiatric nurse.

"They were decent people," he says. He has an older brother and an older sister, but is extremely protective of their privacy and will say only that they are passionate readers and love the theatre.

Becoming an actor was not the masterplan. He went to drama school at the suggestion of a girlfriend. "I didn't think I'd do acting for money or a living. I was just postponing something unpleasant. Being a writer was always scheduled - very conveniently - for any time but now."

But he always got work. First in the theatre, working with playwrights such as David Hare and Tom Stoppard, and then moving into television. There was a steady series of jobs over the years. Films like Still Crazy, Lawless Heart, State of Play, culminating in Richard Curtis's Love Actually. It was his breakthrough role as an ageing rock star - reprising his part in Still Crazy with Billy Connolly - that got him a lot of attention. After that, people could put a name to a face. The film was a big hit in America and was followed by The Girl in the Café, The Constant Gardener, and his role as Davy Jones in the Pirates of the Caribbean.

"So I didn't think, 'Finally,'" he says in response to late success, "because I've always done okay. I've paid the rent. I'm just extremely lucky. It's all a surprise to me. I'm surprised to get away with any of it." It's possible he's being coy, but it seems entirely plausible that he is genuine.

We move around the exhibit. He lingers in front of an album cover: Highway 61 Revisited. "This was so mysterious at the time. People didn't do covers like this."

We pass by photos, rows of 45s, handwritten lyrics, and arrive at the booths. A cubicle provides a space to listen to an album and you can press a song and hear Dylan singing. There is just enough room in the booth for two of us and Nighy presses the button for She Belongs to Me. Immediately he begins to sing along. He shuts his eyes, sways, and is lost for a few seconds. He has a sweet voice. "She never stumbles, she's got no place to fall... " He cuts himself off after a few lines - conscious of where we are.

What does he think of when he hears this?

"It takes me back to when I was a kid. I just dig the sound. It's a love song - and I like the fact that she wears an Egyptian ring that sparkles before she speaks." He presses Love Minus Zero - Dylan's voice fills the booth. Nighy knows every word. "I listen to this all the time."

He has an iPod and people "were kind enough to put stuff on it". And what's on it? Mostly the Stones, Bob Dylan, Marvin Gaye, Otis Redding.

We move to another booth. A song comes on. "I left home on the strength of this album. I threw my suitcase out the window. I could have used the front door but I didn't want to have to run it past my dad. Bob calls it that highway sound. I was young. I just wanted to run. It's natural. But the trigger was this album. It was something about the harmonica. That 'mercury' sound, he calls it. I used to hitchhike everywhere. I like being in between places. I used to love being on tour. Everyone used to complain about it, but I loved it. I love trains. Preferably at night. It's fabulous. Preferably in the rain. The rain is best. Night-time rain on a train with a little wind. And a good book."

Going where? "Who cares? Preferably somewhere you've never been. That's ideal."

We are sitting downstairs on a bench in the lobby of the museum and Nighy is apologising. He has impulsively turned my tape recorder off - twice - during a conversation about a subject he's not comfortable discussing.

I had returned to the question I'd asked earlier about the hard times. But I'd been too oblique. He became frustrated - asked me to be specific.

I wanted to know about the toughest time he's been through. It's been written about before, but his answer has been somewhat general and vague. There was a long silence. But he obliged.

"The toughest single thing I've had to deal with is the fact that I have an unhealthy relationship with all things mood-altering - with a particular emphasis on alcohol."

It was an honest, albeit measured, answer. But when discussing it, I used the word "addiction" and he bristled. That was not his word. "I am choosing my words very carefully because I have a responsibility. I give it maximum respect. And the sentence I have just constructed... it's very clear. I put it like that [he makes a box with his hands] and not like that [makes another box]."

The tape stops. I reassure him it will be okay.

"I don't normally do this question," he says. Which is perhaps why he seems so vulnerable and fragile. He is trying to walk that line - to get his point across and not disappoint.

"To be released from that is my greatest good fortune. I have a responsibility. It's really clear."

We are back in the car on our way to the Music Box theatre in Times Square. The light is fading and he tells me he plans to take a nap before the evening's show. "Yes, very rock'n'roll." Then he will have what he has every night - a ham-and-brie sandwich from the deli across the street. He will also have, he stammers, "how do you say it... mottso... ?" Matzo-ball soup? Yes. "But without the balls. The balls are insane. And once you take the balls out, there's no soup."

I point out that it would make sense to order just the chicken broth. "Oh, I didn't know you could do that!" He looks delighted.

There is a single bed in his dressing room, several bouquets of flowers, and a hamper of English chocolate. With Marmite and Yorkshire tea. Maltesers and Aero are in the mini fridge and he offers me a Jammie Dodger.

With only two hours before the show, what's going on in his head? Not a lot. Before the play opened, there was a great deal of anxiety. He explains he was going through what a lot of actors go through - the prospect of letting everyone down and being exposed.

There is, he admits, no real sense of how he is doing. He uses precedence to embolden him: knowing he did it before and didn't get fired.

So now he feels relieved. "Every day this week I've woken up thrilled that it's not last week."

An hour after I leave, a text message arrives thanking me for my patience. And over the next few days, there is an exchange of friendly texts and voice messages. An apology for being a bit scattered. One asking for something he's mentioned to be omitted. One message shares that he has ordered the soup without the balls... and an anchovy salad. The message ends with a question. "Is that too much information... ?