Sitting beneath a picture of Winston Churchill in the gloomy Carnegie Club in Manhattan, surrounded by the swirling smoke of Montecristos, is Brian Cox. Not because he’s a member – although Cox does live in Brooklyn nowadays – but because the place has fittingly been chosen by the publicist of his new film, Churchill. “Everyone’s done it,” he acknowledges of his new role, but there were more reasons for Cox to play the great leader than there were cigars in the prop box.

Twenty years back he’d pondered playing Churchill in a film that was never to be, about his dealings with Franklin Roosevelt and America’s entry into the Second World War. There was the memory of his first wife working on the set of Young Winston 45 years ago. And, of course, for years Churchill was MP for Dundee, the Scottish city from which Cox hails. You could conjure countervailing arguments for not playing Churchill, of course. Cox, who turned 71 at the beginning of the month, had to gain lots of weight and shave his head.

And then there was the prospect of all those cigars. He’d also be risking comparison with John Lithgow, whose Churchill is still fresh from Netflix’s The Crown, and also no lesser stars than Albert Finney and Michael Gambon, who played him in The Gathering Storm and Churchill’s Secret. Cox still hasn’t caught up with the Lithgow interpretation. “He very sweetly sent me an email welcoming me into the fraternity,” he reveals. “That’s John. He’s a very generous human being.”

Though a member of the Garrick Club and considering himself an anglophile, Cox was hardly to the establishment born. His father was a grocer in Dundee who died when he was just eight years old. He mentions almost distractedly that thereafter his mother suffered what was essentially a nervous breakdown. “She was not around. I was on my own,” he recalls.

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His salvation was the London Academy of Music and Dramatic Art where he fetched up at the age of 17. “It was an amazing period, the ’60s. It’s a bit of a cliché but it was that great period of social mobility. There was Free Cinema, there was Albert Finney, there was Alan Bates, Richard Harris. There was Peter O’Toole. All these wonderful iconic actors you could look up to and envy.”

Cox left for America – and Hollywood – in 1995, partly to follow in the footsteps of his heroes but also to escape Britain’s abiding capacity for snobbery. He says he felt it especially as a Scot, just as his friend Anthony Hopkins, who also gave up on Britain, felt it as a Welshman. “Tony Hopkins and I have one thing in common: we are not English,” he muses. “It’s a very interesting thing about the feudalism of English society. It’s about who you are and where you come from, how you operate within that world. It’s the caste system, which still exists and is actually even worse now. I mean it really is – it’s more insidious.”

For Cox, who hasn’t shied from the occasional potboiler (think the Bourne franchise and more recently season two of Shetland), it surely also helped that the focus of this window into Churchill was intensely political.

The film (in cinemas from Friday 16 June) spans the days leading up to the D-Day landings of June 1944 and Churchill’s attempts to offer an alternative, less risky plan to harry Nazi forces. Cox saw at once that, by focusing on his D-Day doubts, the film would offer a layered Churchill, not just the bulldog we learn about at school. “He was extraordinary, like Mandela or Napoleon. He was this man of destiny. And he was a construct,” Cox says.

“The cigar, the whole thing, he was sort of like Hitler and Mussolini. They were constructed characters. His construct was his rhetoric, his way of bolstering the nation with those extraordinary broadcasts, his almost Shakespearean sensibility and language, the V-signs. But there is another Churchill.” This is a Churchill who is far from being gung-ho on the eve of Operation Overlord, when close to a million Allied troops amassed on the south coast of England ready to ship out to the French coast. He had terrors that they might be going not to victory but to certain slaughter, something he had seen before following the loss of 56,000 soldiers under his calamitous command in the Battle of Gallipoli during the First World War.

This was the “demurring” Churchill, as Cox puts it. “There’s a Churchill who is more private, not quite as sure of himself. A Churchill who is a depressive – with his ‘black dog’ – and who drinks like nobody drinks,” Cox offers, adding that the prime minister was “tortured by the Gallipoli landings”. The new film opens with the compelling image of Churchill on a beach imagining the incoming tide turning red. Cox notes that straight after Gallipoli, Churchill resigned as First Lord of the Admiralty and went to the western front as an officer with the Royal Scots Fusiliers. “It was a form of penance, I think.”

Other elements were hiding behind the “Churchill construct” that Cox was eager to explore, including his resemblance, physically and to an extent emotionally, to a baby. Cox looks up at the photograph on the wall above him. “All babies look like Churchill and Churchill looks like all babies,” he suggests. “The cigar is like thumb-sucking and there is that cantankerousness of a child.” He was also informed by a comical streak in the leader. “There is a Fatty Arbuckle quality about him.”

Biopics of Churchill come and go, with Gary Oldman playing the politician in Joe Wright’s Darkest Hour, due in January. Going back to 1972’s Young Winston, Cox’s first wife, Caroline Burt, helped train non-native actors in the mysteries of British etiquette, including Anne Bancroft in the art of serving tea. That we are seeing so much of Churchill on our screens now, Cox argues, is a function of what’s missing in our own political leaders today, on both sides of the Atlantic.

"The whole Churchill phenomenon is because of a zeitgeist about vision and principle,” Cox says. “It does say something about the vacuum that is there at the moment, especially in our country.” (He mutters about the “awful Michael Gove, Iain Duncan Smith, David Davis, Theresa May.”)

Cox, who supported independence for Scotland in 2014 and who lent his voice to the election broadcasts for Labour’s winning campaign in 1997, is only getting started.

“Churchill would have thought Donald Trump was an idiot. He was a man of principle, and I don’t think he would have liked Boris Johnson, who wrote a book about him. Johnson thinks of himself as Churchill, but he hasn’t got the gumption of Churchill. He is an opportunist, and he is about as deep as a blackhead.”

Cox is a fan of Nicola Sturgeon, but not sure the time is right for another independence vote. “I think it would be best to sit on it for a while,” he says, noting the risk of “neverendum” syndrome. Cox’s self-imposed exile from Britain was not just about the vagaries of the class system. It was also about getting work, in Hollywood especially. It’s a choice he thinks British actors don’t need to make anymore, partly because of the rise of companies like Netflix and Amazon making high-quality shows, for which actors can drift in
and out of the US as and when they get contracts.

“You don’t have to put down your roots in the way that I did. And the Hollywood thing has sort of dissolved as more and more TV is being made in New York.” He has a “hidey hole” in London, but his sons with his second wife, Nicole Ansari, would veto moving back full time.

Often reluctant to view his own work, he made an exception for Churchill, partly at his wife’s urging. Is he happy with it? “Yeah, I am actually. I think that what happened on the ground is up there on the screen.” As for the cigars, they didn’t trouble him at all on account of some trickery of the trade. “Electric cigars!” Cox reveals. “Different lengths of electric cigars, designed for us – brilliantly.”

Churchill will be released in cinemas on Friday 16th June