“Impressive, isn’t it?” says Mr Jude Law, peering out of the window at the great, majestic plane tree that rises from the courtyard and soars over the top of Bourdon House, the former London residence of the Duke of Westminster and the current home of Alfred Dunhill. “They can’t get rid of it. They tried when they first bought the place, but it’s protected by some funny old legislation.”

He’s right, as it turns out. The tree is right in the middle of a conservation area. When the new owners of Bourdon House approached the council about relocating it, they were told that any action resulting in the death of the tree would result in a fine of £10,000 – for every window that overlooks it. In the street outside, there are literally hundreds of windows, and this enormous tree is visible from almost all of them. Any mishap would have potentially cost Alfred Dunhill millions. So, the tree stayed where it was. “Best to keep the neighbours happy, eh,” says Mr Law, turning away from the window with a grin and segueing straight into another story – this one about the Duke of Westminster and Ms Coco Chanel.

He does like an anecdote, Mr Law. And he tells them well, too, gesticulating animatedly and grabbing your attention with the skill of a natural raconteur. When he gets particularly caught up in a story, as he appears to be doing right now, a familiar glint appears in his eye. It’s that same, mischievous glint that seduced cinema audiences in his breakthrough role as the errant playboy Dickie Greenleaf in The Talented Mr Ripley – and it draws you in, just as it did then. It holds you. It compels you to sit and to listen.

Just as well, really, because today Mr Law has a story to tell. It’s a story of a treasure hunt beneath the waves – of a doomed ocean voyage and a crew of desperate men. In Black Sea, the new movie from Mr Kevin Macdonald, director of The Last King of Scotland, Mr Law plays Captain Robinson, a laid-off submarine captain who goes in hunt of a sunken ship rumoured to be laden with Nazi gold. (Yes, that really is the plot.) Backed by shadowy employers and stuffed into a rusting Russian sub with a ragtag band of mercenary seamen, the scene is set for everything to go horribly and spectacularly wrong. Which, in due course, it does.

The submarine movie is classic cinematic fare, for obvious reasons. Men trapped in an enclosed space with a limited oxygen supply? If you can’t create a sense of tension here, you can’t do it anywhere. But Black Sea is more than just tense. Mr Macdonald, an Oscar-winning documentarian who previously directed Touching the Void, has taken inspiration from the work of directors such as Mr John Huston and Mr Henri-Georges Clouzot to create a movie that drips with dread throughout.

“He’s a fine film-maker, Kevin, well-versed in the history of film,” says Mr Law, plonking himself down on a plush red sofa. “He and Dennis [Kelly, the writer] looked back at films such as The Wages of Fear [by Clouzot] and The Treasure of the Sierra Madre [by Huston] – stories of desperate men in desperate situations. John Huston was a big influence – I personally likened my character to Ahab, the captain [played by Gregory Peck] in Moby Dick. He’s a man driven to the point of obsession, with nothing to lose and everything to gain.”

Wearing heavy stubble and a heavier expression, a gruff, rugged Mr Law gives an intense performance as the captain – a man supposedly some five to 10 years his senior. “It required a certain gravitas,” he says of the part. “It’s not something I could have done in my twenties or thirties. Having recently turned 40, I feel that I’m only just reaching the stage where I can do this sort of thing justice.”

It has been a long time coming for Mr Law, who grew up in Lewisham, South London to “am-dram” parents and has been around the stage for as long as he can recall. He joined the National Youth Music Theatre in his teens and broke into TV soon after. His cinematic debut came at the age of 22 in 1994’s Shopping, a film in which he starred alongside Ms Sadie Frost; she was pregnant with their first child a year later. They were married another two years after that, and went on to have two more children before divorcing in 2003. The next decade was a tumultuous one, involving an engagement to Ms Sienna Miller that fell apart under the spotlight of the tabloid press, and the birth of another child to Ms Samantha Burke, an American model.

His acting career, meanwhile, seems to have developed to mirror the progress of his life. He admits to having always been fascinated with the idea of getting older – and projecting this ageing process onto his characters. “I tend to think of it in terms of Shakespeare,” he says. “You can’t play Prospero in your twenties. And you can’t play Lear. In your twenties, you play Romeo, you play Hamlet. And maybe you progress to Coriolanus, to Henry V. They’re like hoops you have to jump through. Keep going, and you’ll get to Prospero, you’ll get to Lear. But you can’t rush it.”

A leaf through Mr Law’s cinematic CV will reveal a time not too long ago when he was definitely more of a Romeo than a Prospero. As Lord Alfred Douglas in Wilde, he was the classic, costumed Pretty Young Thing. As Dickie Greenleaf in The Talented Mr Ripley he was the quintessential, golden-haired matinée idol. As the robotic rent boy Gigolo Joe in A.I. Artificial Intelligence, he was the very picture of glossy, android perfection. This early trend of being cast for his looks is maybe best summed up by his appearance in the 1997 dystopian sci-fi Gattaca, in which he played a man of flawless genetic makeup – the perfect physical specimen.

OK, so being easy on the eye is hardly the worst fate to befall an actor – but nobody wants to be defined by their most ephemeral quality. And Mr Law was more than just easy on the eye, too. In his day, he was in possession of an almost otherworldly beauty. The late Mr Anthony Minghella, who directed him in The Talented Mr Ripley and a further two times, summed up the young actor’s predicament when he described him as “a beautiful boy with the mind of a man […] a true character actor, struggling to get out of a beautiful body.”

It’s a struggle that might go some way to explaining movies such as 2013’s Dom Hemingway, for which he gained more than two stone to play an ageing, balding, overweight small-time crook. “It was cathartic, just letting it all go,” he says of the role – before going on to express his resentment that such acting opportunities are largely restricted to men. (Mr Law isn’t just giving voice to his inner feminist here: to put his statement in context, there’s a peculiar narrative playing itself out in the tabloid press at the time that we speak regarding Ms Renée Zellweger, who has had the temerity to consider changing her appearance as a way of safeguarding her career prospects.) “The plight of women over a certain age is a bit of a running gag in the movie industry,” he says. “Not a very funny one, admittedly.”

Of the tabloid press – his bête noire – he’s as coldly dismissive as you’d expect. After years of intrusion into his private life, which came to a head recently with his involvement in the Leveson Inquiry into media ethics, it seems that all he wants to do is move on. “I no longer let that stuff in,” he says. “I honestly don’t know and don’t care what’s being written about me. If people want to buy into it, then they can. I just try to live a normal life now.”

Isn’t it a little idealistic, though, as a movie star, to even expect to be able to do that? “It’s my right,” he replies. “Being free to go out – to a restaurant, to the theatre, or even just to a gardening centre – is my right. That’s what living is. So that’s what I do.”

“Live a normal life.” It doesn’t sound all that complicated, when you say it out loud. It’s only now, though, after half a lifetime of trying, that he finally seems to be getting there. As he gets up to leave, he takes a quick turn around the room where the Duke of Westminster once wooed Ms Coco Chanel, and glances out of the window once more at the old tree that stands guard outside. He’ll be 42 in December, with four kids and another on the way, and he’s easing himself free of the burden of that impossibly beautiful face. He’s free of nuisance, free of noise, free to immerse himself in his craft. Free, finally, to be judged on his acting alone. And he seems happy. Resolutely, determinedly so.

Black Sea is just the latest in a long line of submarine movies – a genre known for suspense, claustrophobia and really, really melodramatic titles, such as We Dive At Dawn and K19: The Widowmaker. Here are our top six.

Mr Clark Gable plays a US submarine commander obsessed with wreaking his revenge on the Japanese destroyer that sank his previous command. Think Moby Dick meets Mutiny on the Bounty, only underwater. Mr Burt Lancaster plays Mr Gable’s No.2, who is bitter about being passed over for command. With Mr Don Rickles rounding out the cast, this is a mantastic Netflix night in. Allstar Picture Library

A rescue mission to an Arctic weather station aboard the USS Tigerfish with Messrs Rock Hudson, Ernest Borgnine and former Cleveland Browns running back Mr Jim Brown? That sounds like entertainment to us. Snap Stills/ Rex Features

Journey with the Fab Four as they attempt to save the underwater realm of Pepperland from the Blue Meanies. It’s Fantasia on acid. OK, Fantasia on more acid. Snap/ Rex Features

A gripping WWII action flick – but one perhaps best remembered for the affront it caused to British war veterans by suggesting that it was the Americans, rather than the British, who recovered the Enigma machine. Moviestore Collection/ Rex Features

A German U-boat crew heads out on a mission in the Atlantic. A taut, nerve-shredding thriller and a dispassionate exposition of the horrors of war, no film gets to the crux of the submarine genre quite like Das Boot. The German director Mr Wolfgang Petersen was nominated for an Academy Award and went on to become the Hollywood helmer of In the Line of Fire, The Perfect Storm and Troy. Moviestore Collection/ Rex Features

"The three most powerful men in the world: the President of the United States of America; the President of the Russian Republic; and the Captain of a United States ballistic missile submarine.” Whatever you think of that as a statement of fact, it makes for an undeniably enticing movie premise. Mr Gene Hackman is the captain wielding the power, Mr Denzel Washington the executive officer intent on stopping him from misusing it. Featuring a script peppered with references to classic sub movies such as Run Silent, Run Deep and The Enemy Below – for which we have to thank an uncredited Mr Quentin Tarantino – this is one underwater action flick that knows exactly what it is. Kobal Collection