Over coffee and biscuits in a Soho hotel, the actor who played Billy Liar is showing me a picture of his dog on his iPhone. If this was not weird enough, Tom Courtenay then points out that Stanley, his seven-year-old pointer, is gazing longingly at Colin Firth on a Sunday supplement cover. “We did a film together … me and Colin, that is,” 81-year-old Courtenay explains with a wink. “Extremely unsuccessful but very enjoyable; we laughed all the time. So we now have a running joke on these things,” he says, wiggling his phone, “which is nice. I also sent him another where Stanley was deciding between him or Dustin Hoffman.”

To spend an hour with an actor whose career is practically as long as modern British cinema is a disarming experience. It’s disarming because youthfulness still shines in his glossy, green-blue marble eyes. Still present too is the impish melancholy that made Courtenay famous in his second film, 1962’s The Loneliness of the Long Distance Runner, and Billy Liar, his third, in which his angry young man in Yorkshire ducks off taking a fateful train to London and freedom.

But Courtenay’s current career is as rich as his past. Revived by 2012’s retirement home comedy-drama Quartet, he followed up with a 2015 TV thriller, Unforgotten (winning a Bafta in the process), and gave an astonishing performance in 2016’s 45 Years, for which he won a Silver Bear at the Berlin film festival. The angry young man is hot property again. Later this year comes the Hatton Garden heist comedy King of Thieves, in which he stars alongside Michael Caine, Paul Whitehouse and the man who he calls “Raymondo” (Ray Winstone). “And Jim Broadbent’s there, too,” he says quickly. “I was emailing him about hearing aids this morning.”

Courtenay is here today to talk about The Guernsey Literary and Potato Peel Pie Society, a glossy, big-budget second world war romance directed by Four Weddings and a Funeral’s Mike Newell. He is the first person we hear in it, singing drunkenly as he breaks the curfew imposed by the island’s occupying Germans; then we see him vomit on a Nazi soldier’s boots. When he is caught with his friends, they say they are a book society – the pie is a drunken invention of Courtenay’s character, Eben Ramsey – so they then have to form one, leading to books bringing them a new kind of life.

“That’s what I liked about the film,” says Courtenay. “And it says a lot about tyranny. How many books has Trump read?” His eyes widen like goldfish bowls. He’s a big reader himself, having just finished Ivan Turgenev’s Fathers and Sons, and raves about David Foster Wallace (“Astonishing”).

Courtenay’s early life was framed by the second world war. He was two when it broke out and he endured most of it from his home in heavily bombed Hull, where he lived near the fish dock; although, knowing no different, he loved it. “We’d go looking for shrapnel. In the Anderson shelters, I used to love getting up and giving them a song; it was exciting.”

This love for performance endured. One of only two boys from his class of 50 to go to grammar school (“That shows how poor that area was”), he enjoyed everyone going quiet while he read the lesson at prayers, but didn’t think properly about acting until his late teens. Success came quickly: after studying at Rada, he was spotted at 23 in an Old Vic production of The Seagull. Two years later, The Loneliness of the Long Distance Runner opened in cinemas to rave reviews.

But it was a terrible time, Courtenay says. “I was quite close to a nervous breakdown, because I just felt guilt about my parents. My education meant so much to them, and the money ... Dad used to give me little subs.” Then, in 1962, Courtenay’s beloved mother, Annie, died of breast cancer. His 2001 book, Dear Tom: Letters from Home, movingly chronicles the correspondence between them in the time just before her illness, and, until recently, he “couldn’t bear looking back” at that time and his earlier film roles.

That insecurity started to change in 2015 when, for the first time in decades, he saw a screening of The Loneliness of the Long Distance Runner at a film festival. “I’d always worry about what I didn’t have back then, like technique and assurance. But when I watched, I was astonished at something I realised I did have back then: sheer, raw passion.” He gasps dramatically. “Gosh!”

More high-profile roles followed, including an Oscar-nominated performance as the revolutionary Pasha in Doctor Zhivago, before Courtenay turned away, Billy Liar-style, from Hollywood’s calls, preferring to find solace in theatre. He has turned down some huge roles, he says, “including one in the last few years where the chap who took it won an Oscar”. He won’t reveal who.

Courtenay was also Oscar-nominated for 1983’s The Dresser alongside old Rada pal Albert Finney, but the jobs that followed it were cushy, lower-quality gigs. There was the 1987 Peter Falk heist movie Happy New Year (“although that bought me a house in the Lake District … Albert called it Columbo Cottage”) and a turn as Bill Cosby’s butler in the flop spy parody Leonard Part 6.

“He was sweet to me,” says Courtenay when pressed about the recent Cosby revelations. “But there was a certain strangeness of behaviour. I remember us having dinner, and him insisting on us sitting on the landing of the hotel so that people could see us.”

The “us” refers to Courtenay and his second wife, Isabel, a stage manager whom he met during The Dresser’s initial theatrical run in 1980. They married in 1988, and he mentions her constantly; she encourages him when he’s feeling unsure. “I’m a bit of a glass half-empty merchant, I’m afraid, which is where Isabel comes in: she’s much more half-full. I mean, I didn’t want to go to our film premiere last night, and she said: ‘Come on, Tom, it’ll be fine,’ and it was.”

Recovering from prostate cancer in 2004 spurred on Courtenay’s later career, he says. “People say, “Oh, you shouldn’t talk about it, but I’ve done some of my best work since I was diagnosed. Then there was my new hip in 2007, my eyes, 2018 ....” The latter was initially a cataract operation, he says, but then his doctor realised Courtenay had never actually been able to see colour properly, as a result of childhood scarlet fever – so he fixed it. “And now I can’t shut up about it,” he beams. “I bought a brown T-shirt in Glasgow a while ago, and now I’ve realised that it’s plum! It’s incredible, really. I’ve got all this colour in my life.”

He is also comfortable with being described as a veteran: “I’m 81! There’s no escaping veteranism.” Plus, getting older has its benefits. “I really like pottering about. I’m free after this, for instance. I might go and buy some jeans. They’re my new thing.” Then he and Isabel will sort out a hotel in Guernsey, he says, for the second premiere being held there; and they will go by boat, so they can also take Stanley.

Leaving our meeting, Billy Liar puts on his old man’s flat cap, gives a hug goodbye, with those green-blue marble eyes both peaceful and alive, as he heads off to board another London train.

The Guernsey Literary and Potato Peel Pie Society is in cinemas now.

• This article was amended on 20 April 2018 to remove an editing error which mistakenly introduced a comma into the sentence “in which his angry young man in Yorkshire ducks off taking a fateful train to London and freedom.”