I’m going in soft with Daniel Mays and starting with an easy question. Has he ever thought about committing a random racist crime? Well, he is an actor, this is an interview, and it’s taking place shortly after the publication of That Liam Neeson Interview.

We are after more than just some puff about the latest film these days. When we interview actors, we are looking for headlines and shockwaves.

“You’re not going to be getting a Liam Neeson soundbite out of me,” says Mays. “That was an extraordinary admission, wasn’t it? A ridiculous thing to come out with.” No sympathy from Mays. And phew, at least he recognised the reference, and doesn’t just think that I think he’s a racist. Is he, though? That’s my second question. “NO! I am not. I’m firmly in the non-racist camp.”

One more icebreaker then: who does he want to kill? “I’m a very placid human being,” he says. “I don’t want to kill anyone. I guess I have played a lot of bad people in my career, so frustrations or angst can come out in any given role.”

Back to his latest film, then – Fisherman’s Friends. Not a story about extra-strong lozenges, but a heartwarming British comedy based on the true story of a bunch of Cornish fishermen and singers of sea shanties who got signed to a label and made a record that did well. It has been romanticised, with a love story thrown in for extra feelgood. Mays plays the fish, or at least one out of water: a London record executive abandoned by his fellow stag-doers in Port Isaac.

“Did you enjoy it?” Mays asks me. Hang on, who’s asking the questions around here? I did, I tell him. It’s likable, family entertainment: think The Full Monty, Calendar Girls or Swimming With Men, but with less exposed flesh. “It’s a project that caters for the masses,” he says. “I’m not afraid of that. It’s a box that can be ticked. I think what the film does achieve is pathos.” Yes, I got pathos.

We are drinking frothy coffees in a London members’ club. Taller than you would expect (Mays, not the coffees. Mays says he is taller than everyone expects), currently bearded and refreshingly un-arsey, he says the role of cynical urban music exec plays to his strengths as an actor. Which are? “God, that’s a difficult question,” he says. “I don’t know if it’s a level of commitment to things. I can remember Mike Leigh saying to me: ‘The thing I love about you, Danny, is it’s no holds barred. You just throw yourself straight into it.’”

Leigh, who cast Mays as an abusing thug in 2002’s All or Nothing, comes up a lot in our chat. Now 40, Mays owes him for getting his career up and running, for making him the actor he is. “I love that element of investigating something,” he says. “That all comes from Mike Leigh – trying to find a hook, trying to find little nuggets of information you can apply. And it’s about just saturating yourself in whatever world you’re in. Something will instinctively come out, whether it’s a gesture or a mannerism. It’s about being specific.” When Mays got into character as Jason in All or Nothing, people were scared to go near him, and that included the makeup artist.

Two years later, he starred as Imelda Staunton’s son in Vera Drake, Leigh’s 2004 film about a woman in the 1950s who performs illegal abortions. He has tried to take his saturation ideas to everything he has done since, whether villain or cop (lots of cops, actually), son or dad, train robber or great diarist. Memorably, he got inside Ronnie Biggs, breathing life and adding layers of complexity to the character, alongside Sheridan Smith’s Mrs Biggs; and as Sgt Danny Waldron, he looked like he was going to be a brilliant protagonist to the third series of Line of Duty until – criminally – Jed Mercurio killed him off in the second episode.

He’s just as proud of his role in last year’s gut-wrenching drama Mother’s Day. He played Colin Parry, the father of Tim, the 12-year-old boy killed by the IRA in the Warrington bombing. He felt he owed a strong performance to the real people affected by the blast and events and found the drama especially poignant given that his son, Milo, was the same age as Tim when he died. He is equally proud of Guerilla, the mini-series set in London in the 1970s against a backdrop of British black-power movements. “I love being involved in projects which look at the world we live in, society around us, sparking debate, asking questions.”

Mays isn’t from a thespy background. He grew up in Buckhurst Hill in Essex. His dad was – still is – an electrician, his mum was a cashier in a bank. “I was always doing dancing, or performing, or doing impressions of Frank Bruno or Prince Charles.”

Go on then, give us your Frank. “No, I can’t do that now, all it was was the laugh.” He breaks into that deep Bruno chuckle: “Hee hee hee.” Yeah, not bad, although I’m not sure he has fully saturated himself in Bruno’s soul.

So, although his dad needed a bit of convincing that it was a good idea, Mays went to the Italia Conti stage school and later Rada. Theatre followed (lots of great stuff at the Royal Court), a few bit parts in soaps and pilots, and then Mike Leigh. His three brothers, meanwhile, became a cricket groundsman, a salesman and a money trader.

Can we have Prince Charles please, now? “No, I mean …” he bumbles, poshly. Again, not bad. Apart from once playing Samuel Pepys in ITV’s The Great Fire, Mays doesn’t get to play the upper classes much. He has spoken out against favouritism towards public school actors in the past, although peak-posho was a couple of years ago, he says, and seems to have tailed off. He has been involved in a Rada initiative, trying to find more kids not from Eton, nor even Italia Conti. “I think that is the most important thing – that you are getting authentic, working-class kids, giving them an opportunity, allowing them to try. You have to have a platform within this industry where those stories need to be told.”

A case in point is something else he’s got going on at the moment. Two For Joy is a film directed by photographer Tom Beard, which had a limited cinema release last year and is now available on video on demand. Mays plays a caretaker in a seaside caravan park and the film touches on mental health, abandonment and parenting. One of the three kids in it – a boy named Badger Skelton who puts in a mesmeric performance while barely saying a word – had never acted before.

So what is currently getting Mays riled? Brexit, unsurprisingly. “I went to stage school, I went to Rada, I’ve been in this London bubble for as long as I can remember, which is involved with being as inclusive and accepting of any people from different countries, different walks of life, different religion – that’s who I am. To pull up the drawbridge, you know, we are an island race. It’s completely alien to me.”

He recently went to a reunion of his old football team in Essex. “Invariably, it got round to Brexit, and so many people there – mates I’d not seen for years – were of the mindset: we want our country back.” Just 12 miles from where he now lives in London, but a world away. Oh, and his parents wanted out of the EU, too.

That is interesting, but it’s hardly Neeson is it? One last try, is he sure there’s nothing he wants to get off his chest? Something from back in the day, in Essex perhaps? No?

So where are we then? An excellent, hard-working, surprisingly tall but well-grounded actor diverges from parents and past on politics, and is neither racist nor murderous. Still, he does do a passable Frank Bruno.

Fisherman’s Friends is released on 15 March.