Michael Gambon and Lindsay Duncan on Churchill's Secret

“Oh come on,” says Duncan, who plays Churchill’s wife Clementine to Gambon’s Winston. “He isn’t well... he’s had a stroke!”

The mild stroke, which begins the film, came at Number 10 Downing Street on 23 June 1953, temporarily paralysing the then 78-year-old Prime Minister, who was whisked away to Chartwell, his country home in Kent. Remarkably, all of this was kept from the public and Churchill recovered under the care of a nursing team and his formidable wife.

In real life, too, Duncan seems to be looking after her on-screen partner. She finishes Gambon’s sentences and shouts “thingumajig” if a name threatens to elude him. Which is fair enough at his age, you might think, but it goes deeper. Last year Gambon was obliged to give up theatre work because he was forgetting his lines. At the time he told RT, “it broke my heart” and today, wearing dashing mustard socks and a blue felt waistcoat, he relives the moment when he realised the game was up.

“Me and Tom Hollander were rehearsing,” he says. “Tom did his lines and I had someone in the corner speaking mine into a plug in my ear.” It sounds desperate – and it was.

“The speed of talking, of walking around, it just wouldn’t work,” Gambon says of the ill-fated rehearsal. “We spent a morning doing it and it ended up a disaster. So I said to Tom, ‘This isn’t going to f****** work – we can’t do this.’” Gambon can still perform some theatre. He cites Samuel Becket’s Eh Joe in which he says almost nothing, and Krapp’s Last Tape where, “I’m at a table in the middle of the stage and the audience don’t know, but the lines are there.”

He may be weakened, but Gambon remains ever-present in the television landscape he has dominated since he starred in Dennis Potter’s The Singing Detective in 1986. In February 2015 he led the BBC’s adaptation of The Casual Vacancy by JK Rowling; and followed that in April with a lead role in the Sky Atlantic drama Fortitude.

The 65-year-old Duncan, dressed entirely in black, who will contrive to fume and cackle and yet remain utterly elegant, appeared with Gambon in Stephen Poliakoff’s Almost Strangers in 2001. She will appear in Poliakoff ’s Close to the Enemy later this year, and can claim two Olivier awards and a Tony for her masterful stagecraft.

The pair are quite a catch, then, but Gambon says he was surprised to be offered the part.

“It was a shock when the director said, we want you to play Churchill,” he says, his speaking voice resonant, but so hushed it’s almost inaudible. “I thought, Oh Christ almighty. I know of him! I said I’d think about it.” Gambon took it, of course. “Well you do, don’t you?”

Churchill has previously been played on TV by Robert Hardy and Albert Finney. “I remember Albert taking his clothes off and laying in the bath,” says Gambon. “I thought, ‘I don’t want to do that’. Oh no.” Gambon keeps his clothes on, but although he has the props you would expect – a cigar, the occasional glass of something reviving – his performance doesn’t slip into full “We shall fight on the beaches” mode.

“You can’t do that,” he says. “You do fractions of it, so you sound a bit like him, but the rest is acting. It’s hard to explain. It’s just what I do.”

The drama is an adaptation of Jonathan Smith’s novel KBO: the Churchill Secret. KBO stands for “keep buggering on”, Churchill’s answer to any of the many challenges life threw at him. In 1953 Clemmie very much wanted her husband of 45 years and father of their four troubled children to stop buggering on and retire, nonetheless she assisted in a cover up.

“I think they were devoted to each other,” says Duncan. “It was a profound relationship. He always felt he must go on and on and that was very difficult for her. She often gave advice that he didn’t listen to. But I think they really were emotionally connected and it was a very long marriage. And they wrote to each other all the time. I found that so touching; they expressed everything in those letters – love, anger, frustration and desire.”

Duncan suggests that filming is tougher for Gambon just because of who he is. “I think if you are well known you feel under more scrutiny,” she says. “I’m not flattering him emptily, but people get very excited about Michael being on the set. You hear them saying, ‘I’m going to see Michael Gambon today’. It’s a pressure.”

Given his memory problems I wonder how Gambon gets through the shooting. “I look at the director to see if he’s happy and he gives me a few notes. That’s how I get through it. It’s the only way, isn’t it?”

Duncan claims the only help she offered Gambon on set was by “Turning up. We didn’t go off into corners together and say: what do you need me to do?”

She may be an astonishingly accomplished actress, but Duncan even admits to her own doubts when filming begins.

“You arrive and you see a sea of strangers and you are going to be intimately depending on them. The awful thing is you think, s***, this is day one, and we are not going to have another day one because there’s no money but you make that commitment and at the end I nearly always feel, oh God, if I knew then on day one what I know now it would have been slightly different.”

Watching her Clemmie it’s hard to see what she could change. It’s a cool, perfectly contained performance that breaks apart on the revelation of a family tragedy that’s not very well known – the loss of the Churchills’ three-year-old daughter Marigold to septicemia in 1921.

“Winston doesn’t want to talk about it, he’d rather not think about it,” says Gambon. “It’s a male reaction – cut it off. Live with the sorrow of it yourself and keep it quiet.”

I ask Gambon if he is like that himself, to which he responds, a little sadly, perhaps, “I don’t know what I am like.”

Clemmie did want to talk about it and Duncan plays her as a woman who struggles to keep her emotions buttoned up.

Duncan has known family tragedy herself: her father was killed in a car accident when she was 15, but she refutes any suggestion that she draws on her own backstory for inspiration.

“No, I don’t do that. I don’t dig into my life experience. It feels weird and it feels dishonest. I do hope I have a sharpened sense of human behaviour, but to me, my life is my life. A director once whispered in my ear, ‘Draw on something personal.’ I was furious. I said, ‘Don’t ever say that to me again’.”

“Absolutely,” agrees Gambon. ‘I’ve been whispered to by directors, who say, ‘Pretend your mother’s just died.’”

I feel Duncan’s gasp of anger before I hear it. “No!” she says. “Really? Really?”

“Yeah,” says Gambon. “You think, bloody hell, it’s got bugger all to do with it.”

“That’s out of order!” says Duncan. “It’s insulting, a manipulative and crass thing to say because an actor’s imagination is one of their skills.”

Don’t you need to empathise with the character?

“No, it’s a terrible idea if your first thought is, I’ve got to love my character,” says Duncan. “You’ve got to learn who they are.”

Gambon agrees. “That’s right; they can be a total s**t, can’t they? What you have to do is play it at as real as you can.”

Given his problems, is Gambon confident he can keep on playing it real?

“I am. I couldn’t play a man who is screaming and shouting and doing somersaults – but I can keep on doing this.”

For how long?

“Until I am dead,” he says. “Until I am dead.”