It's after 5.30pm and Timothy Spall is running late.

Very late. Not that he has grown too big for his boots, I should add. Humble, humane and good-humoured, Spall is the antithesis of the egotistical actors that populate the boulevards and billboards of Hollywood. No, the reason he has let time tick by is quite simple: he is talking about his latest film, Mr Turner. That's Joseph Mallord William Turner, the celebrated early 19th century English Romantic painter, who finally has a film that befits his status as one of the greatest artists Britain has ever produced.

Spall can't stop talking Turner, and a day of press has seen him overrun wildly. "I am not bragging but I do know quite a lot about the character," he says. And so it proves, the actor displaying an almost encyclopedic knowledge of the man. He didn't just read the biographies; he gorged on discourses written by Turner's critics, peers and mentors. By the end, my head is spinning with references to Joshua Reynolds, Claude Lorrain and Thomas Gainsborough. You could probably deliver a lecture in art history, I say. "I'm not by nature academic," he replies, "so I really had to go and get a brain from somewhere and screw it into this one."

His excitement is understandable: in a career that has seen him go from Auf Wiedersehen, Pet to working with Tom Cruise in such films as Vanilla Sky and The Last Samurai, his portrayal of Turner is unquestionably the most masterful performance of his life. Certainly the Cannes Film Festival jury thought so, awarding him Best Actor earlier this year. "No word of a lie, I was one of the most surprised people in the world," he says. When he got the call to return for the prize-giving ceremony, "I was in a boat yard in northern Holland on the Ijsselmeer, with my hand up a tube covered in grease, fixing my boat."

Spall, 57, then launches into a wonderfully long, hilarious anecdote about his crazed journey back to the film festival, where he and his wife Shane were picked up at the airport and chauffeur-driven "like we were the king and queen of Nice" with two police outriders, "waving down all these Maseratis, Porsches and Rollers". Amid all this madness, "I said to my wife, 'I think things are looking up, darling.'" He had a speech written out on his mobile phone, but the battery died. In the end, he delivered a heartfelt seven-minute meander. "I went on a bit," he concedes.

If Spall is too modest to say what it means to him - he has been nominated five times for a Bafta and never won - a few weeks later, I speak to his son, the actor Rafe Spall, who calls his father's performance "a staggering work of heartbreaking genius". How did he feel when he heard about the Cannes triumph? "I was extremely, extremely moved. He is a national treasure and is one of the greatest actors we have got and he has never won an award [of note]. So to see him being recognised in this way … It means a great deal to him and a great deal to my family."

In the past, Spall has been quietly seated next to greatness. Three times he has played Sir Winston Churchill, including the Oscar-winning The King's Speech, an "extended cameo" that saw him obsessively pore over the former PM's speeches as preparation. But of course everyone only remembers Colin Firth in that film. We stray on to Harry Potter, the film franchise in which he played the vermin-like Peter Pettigrew. "It's the smallest part I've ever played and, internationally, the one I get most recognised for. I walk into a lift and grown men say, 'Oh my God - are you the rat guy?'"

There's now a chance that Spall might be nominated for the first Oscar of his career. "I am in that weird position where people are talking about all that stuff. It is difficult because I have got to play the game - and I am [he has even hired extra publicists] but it is one of those things that is an unsaid thing. You do not want to tempt fate. You do not want to stick your neck out. But it has become a bit of a deal in itself. People do campaigns. Really, the whole awards thing … People moan about it until they get one and then they are over the moon. But it would be great for the movie."

Indeed it would, for what is a richly rewarding work that charts the final 25 years of Turner's life in remarkable detail. It will come as no surprise to learn that the director is Mike Leigh, Spall's most frequent collaborator. Their relationship stretches back more than three decades to when Spall played a loutish postman in Leigh's 1982 television drama Home Sweet Home. Their film collaborations include Life Is Sweet, All Or Nothing and Topsy-Turvy, Leigh's earlier period biopic on musical maestros Gilbert and Sullivan.

When it came to Turner, nobody else could have played the part quite like Spall. "I knew he would get the spirit of Turner, but also he is a Londoner, and he has read a lot of Dickens - he understands 19th century London, the spirit of that. I think that is important," says Leigh. Listing his favourite book as The Pickwick Papers, Spall has appeared in several Dickens adaptations: Nicholas Nickleby, Our Mutual Friend and Oliver Twist (twice - as a First Constable in a 1982 TV movie and then as Fagin in a mini-series 25 years on). Just glance at his face, with his pronounced nose, large teeth and double-chin. There is something distinctly Dickensian about him (he calls himself a "funny-looking bugger" at one point during the interview).

Etching Turner with grunts and a pitch-perfect use of early Victorian vernacular, Spall's is a vivid portrait of the artist, but it is under the surface that he really scores, capturing the character's turbulent emotional makeup. "He was a contradiction, like a lot of people. This man was an incongruous contradiction, but then again, so is the world. Like the sun - it is constantly eating itself, it is pulling its whole mass inside itself, and in a sense that is what Turner was doing with himself. He builds this pressure cooker up inside himself, his denials [including that he even had children] and his ability to cut out anything apart from his work … He is a man of destiny."

When Leigh first approached Spall in 2010 about playing Turner, he encouraged him to take a two-year part-time course in fine art under the instruction of London artist Tim Wright. Spall agreed, spending two days a week with Wright, learning the basics. He would regularly visit the 12th century St Bartholomew The Great Church in Smithfield, London, trying to capture Turner's experience of working from a sketch pad, or could be found in the Barbican district drawing Roman ruins. "I am probably about as good as Turner was when he was nine," he laughs, "but he weren't that bad then."

Modesty aside, Spall did it all: life-drawing, still life, speed drawing. He drew more than 300 pictures, watercolours and pastels, including 20 full-sized paintings. The culmination of this remarkable period of study was a precise copy of Turner's 1842 painting Snow Storm - Steam-Boat Off A Harbour's Mouth Making Signals In Shallow Water, And Going By The Lead - an epic about a boat caught in a violent storm that Turner reputedly painted after tying himself to a ship's mast. "I've got that on my wall," says Spall, "and I look at it and think, 'How the f*** did I do that?'"

Next year, the painting will form part of an exhibition at Petworth House, Sussex, where Turner could often be found painting. Even by the standards of a Mike Leigh film, where actors are frequently absorbed in their characters for months on end, building them from the ground up, Spall went above and beyond. Playing Turner is "without a doubt" the most challenging experience of his career. "I knew him and I loved him, but now I know him like he is somebody I know," he says. "When I look at his work, I am still astounded by it. It makes me cry sometimes, it is so, so beautiful and so revolutionary. Turner - as far as I am concerned - is one of the greatest painters in the world."

I ask Spall if there is anything in his career that compares to Mr Turner. The closest he can think of is playing the notorious Albert Pierrepoint in the 2005 film Pierrepoint: The Last Hangman. "I had to really dig deep," he says. He recalls the set, a recreation of the chamber in Wandsworth Prison, London. "It was really disconcerting. And one of the first people I had to execute was one of my son's best friends. They set it up so they dropped and went down the hole. So that was difficult … Again, like Turner, it was a man who was a contradiction. They are lovely to play, these characters, but they are tough on you. You are always thinking, 'Oh God, I am not showing what he is feeling.'"

Spall positively glows when talking about his son Rafe, who has carved out a career in his own right, working with Ridley Scott (Prometheus) and Ang Lee (Life Of Pi). Spall Snr is pleased he sent him to "an ordinary school" in south-east London, near where they grew up. "We didn't have a high-falutin' life," he says. "Just when he came home, there would be quite a few interesting people that you would not normally see knocking about. I have never told him, 'Do this, try that, do that.' It has been much more learning by example, more than anything else. He has really managed to plough his own route - and was determined to do that."

They acted together - once - in a TV version of A Room With A View, playing father and son. "I am deeply proud of him. It makes me want to cry, I am so proud of him. As is his mum. I am proud of all my kids (he also has two daughters, Pascale and Sadie). But the fact he has made it via his own route, and taken it on the chin, and had a few rough rides … He has now got family as well. He is living a proper life. He has not been absorbed purely by the world, which can easily happen to a lot of young actors. And now he has got to the point where if I have had a bad time, it will be the son giving his old dad a bit of a pep talk. It's lovely."

Undoubtedly, Spall's lowest ebb came in 1996 when he was diagnosed with leukaemia, curtailing the career momentum he had built from playing a photographer in Leigh's Cannes-winning Secrets And Lies. He was given days to live, but defied all medical expectations, undergoing chemotherapy in a London hospital. During this horrendous time, he began to think of unfulfilled ambitions. "When I was ill, I started dreaming about boats," he says. Those reveries were the vehicle that inspired his recovery.

After regaining his health, he taught himself to handle a craft, and he and his wife began to navigate Britain's canals and waterways. In 2010, the couple made a documentary called Timothy Spall Somewhere At Sea - "about us discovering our country" on their barge The Princess Matilda. That must be quite relaxing, I say. "I don't know if you've ever been in a Force 6 (gale) … It's bad enough if you are not in charge of the boat, but if you are, it's horrifying." There are benefits, of course. "Put that against being in a calm sea - like this time we were coming out of Aberystwyth, and we were joined by 12 dolphins jumping over the bow of the boat."

While he has always lived near the Thames, he does not quite know where this need for sea air came from. Shane, to whom he has been married since 1981, researched his family tree. "On my side there is a history of east coast sea-goers around the Cambridgeshire, Suffolk borders, up that way."

Born on a council estate in Battersea, the third of four children, Spall came from good working-class stock: his mother, Sylvia, was a hairdresser and his father, Joseph, a postal worker. Early on, he joined the National Youth Theatre, after the acting bug bit during a school production of The Wizard Of Oz, when he played the Cowardly Lion.

His acting education was peerless: the Royal Academy Of Dramatic Art, the Royal Shakespeare Company and then a stint at Birmingham rep. By the time he was 24 he had scored his first film role, a small part in Quadrophenia, but it was in the television comedy about brickies abroad, Auf Wiedersehen, Pet, that he found fame. Playing Barry Taylor, the gormless biker from Wolverhampton, Spall was so convincing he later said it almost torpedoed his career - with casting directors refusing to believe his Black Country accent was not real.

There were some quality collaborations along the way - Clint Eastwood (White Hunter Black Heart), Bernardo Bertolucci (The Sheltering Sky) and Ken Russell (Gothic) among them. Then there were those two Tom Cruise films. Spall has no axe to grind, nothing bad to say about his "sojourns to Hollywood", as he puts it. "From my most simple and truthful experience, the five or six big, big iconic people I have worked with have been charming. Somebody said to me, 'The people you have got to watch out for are not the stars, but the ones on the way up and the ones on the way down.'"

While Spall has worked consistently - even during his convalescence, albeit at a lesser rate - there was a plan in mind. "This sounds like some piece of hokum s***, but in a sense, if you want a long career and you want a film career, you are often defined by what you do not do. It is the things you have to struggle against doing, because they seem like the most lucrative or the easier choice. Sometimes you don't get any choice. It's called unemployment. And actors are always humbled by long periods or rather stultifying periods."

He smiles at this thought. "If you are going to start to feel imperious, it is struck out by the first time when you do not know what you are going to do next." Fortunately, he always has a job - or three - in hand. He will soon reprise his vocal performance for the mutt Bayard in Alice In Wonderland: Through The Looking Glass, the sequel to Tim Burton's $1 billion grossing smash hit. He has also just shot The Enfield Haunting, a three-part drama for Sky based on a real-life paranormal case. "It's not just a horror film - although it is scary," he says.

In it, he plays Maurice Grosse, a British paranormal investigator. "I do not particularly look like him, but there is something about the character I understand. Again, another man of contradictions. Everybody is. Wish fulfilment drama tries to tell you they are not but they are." He laughs uproariously, pointing out that these days even superheroes in Hollywood blockbusters are conflicted.

Who would he play, I ask, if ever he slipped on the Spandex? "What would I be called?" he muses. "Contradiction man!" n

Mr Turner (12a) opens on Friday.