He's at his most monochrome today – his long curly white hair and goatee set against a black T-shirt, short enough to reveal the intricate tattoo on his bicep, complete with a heart and "Pamela" – a reference, of course, to his wife since 1989, the comedienne-turned-psychologist Pamela Stephenson.
This being Connolly, there's always a flash of colour; he lifts his trouser legs, explaining his "preference for very loud and ugly socks" – grey and pink stripes.
He's recently turned 70, though Connolly seems busier than ever. He voiced the King in Pixar's recent Scottish excursion Brave, and over the last year he's been back and forth to New Zealand for Peter Jackson's The Hobbit trilogy. If there's a delicious irony in The Big Yin playing Dáin Ironfoot, the king of the dwarves, Connolly seemed to treat the experience with similar irreverence.
"When I met Peter, he said, 'Have you read The Hobbit?' I said, 'No. And I don't like people who have!' I said, 'I'm not here to make a book, I'm here to make a movie.'"
While he did not make an appearance in the recently released first part, An Unexpected Journey, Connolly is gearing up to return to New Zealand next summer to complete shooting. Although studio blockbusters aren't new to him – he featured in The Last Samurai with Tom Cruise and The X-Files: I Want To Believe – I wonder if he ever marvels at his rise.
"Sometimes," he nods, "as they pick you up at the hotel in the morning in the limousine, and whip you along and you're entering the studio, you think, 'Holy shit, this is real!'"
He felt the same on his new film Quartet, which took him back to the days of Mrs Brown, when he won a Bafta nomination for playing the favoured servant opposite Dame Judi Dench's Queen Victoria. A gentle new comedy set in a retirement home for opera singers, Quartet marks the directorial debut – at 75 – of Dustin Hoffman. Connolly has known The Graduate star for years; they met in Los Angeles, when Connolly performed stand-up at a series of benefit gigs for multiple sclerosis. "He's very easy to be friendly with," says Connolly. "He's got no airs and graces."
While Hoffman had tried to get Connolly involved in a stage production of Waiting For Godot, he then came back with the offer of Quartet. He wanted Connolly to play Wilf, a roguish old charmer who teams up with his fellow retirees to stage a concert performance of Rigaletto at the home's annual gala, proving that they still have what it takes. For Connolly, it meant teaming up with such venerable British actors as Michael Gambon, Maggie Smith and Tom Courtenay, a fact that rather worried him.
"I thought, 'Shit! Maybe I should turn this down?' As a comedian, you're always waiting in terror for owning-up time. Is this the one where I get found out? That I'm not really talented at all. And I remember working with Judi Dench on Mrs Brown and that her massive talent brought out the best in me, and I thought it'll happen again, and I was right. They bring with them, those people of that standing, including Dustin, this aura – and when you're in it, you behave properly."
So what was it like to be directed by the debutante Hoffman, a notorious perfectionist in front of the camera?
"I don't think it is his first film as a director," notes Connolly. "I think he's directed himself for years. When they call somebody a perfectionist, they usually say it as a semi-insult, as if there's something wrong with them. They want to be perfect. I have no right to say this, I don't have the experience, I'm just imagining when he says, 'Can I try it once more?' he wants to direct himself. He's got the idea."
Connolly understood a little of his character's musical leanings; in the late 1960s he left behind his life as a welder in the Glasgow shipyards to become a folk singer in the Humblebums, his first step towards a 40-year career in comedy.
"I didn't like the world of rock and pop – record company guys and music critics," he says. "It didn't appeal to me. The last critique I read about myself, musically, said, 'Connolly with his unfashionably long hair -' And I went, 'F*** off!' That was as far as I got."
He hasn't abandoned the stage, entirely; he still does stand-up – though admits performing live is an increasingly nerve-wracking experience.
"It's getting worse," he says. "I just get deeply anxious about it. I just get this deep anxiety before I do it. It doesn't seem to ease up."
These days, you're more likely to find Connolly quietly sketching away; last March, he staged his first exhibition of drawings, Born On A Rainy Day. He only started two years ago, favouring the abstract. "I did one of God the other day," he smiles, "where he's a welder."
A father of five – two children from his first marriage, three from his 23-year union to Stephenson – he says he has no intention of doing retiring.
"I have always regarded retirement as a kind of obscenity," he says. "I think it's a very good thing: keep working. And I think it's very good for industry, to have wise people in it, instead of new people all the time. More and more, people have more than one career – two or three careers. The Asians have a saying, 'Death seeks hands who have nothing to do.' And it's the truth."
He speaks fondly, very fondly, of Stephenson – revealing how "proud" he was of her when she took to the floor in Strictly Come Dancing, and made it to the 2010 final.
"It was unbelievable," he says, "and she's carried on – she's mad about the tango. She goes out at night and goes to these tango places, and dances with these Bryllcreemed Lotharios. I would love to learn it, but I don't have enough time. I used to jive when I was young. But I've never done the ballroom stuff."
It was Stephenson who wrote his biography, Billy, laying bare his red-raw early days – his mother abandoning the family when he was four; regular beatings from his aunts, who then looked after him and his sister Florence; the sexual abuse from his devout Catholic father, between the ages of 10 and 15. Then there were the days of raging alcoholism – downing, at his lowest ebb, 11 bottles of Chablis in one night. He quit drinking when he was 41 – doubtless the reason why he's still grasping life with both hands.
Spending much of his time with Stephenson in New York now, he doesn't concern himself too much with nationalism and the subject of Scottish independence. This "hippie", as he dubs himself, is an advocate of togetherness, not separation.
"I like the EU. I think it should grow into a world community." But he stops short of mounting his high horse.
"I'm not a great index-finger wagger. I don't think I know the answer. And I think people resent being lectured to by showbusiness people on how to vote – and so they should do." He truly is a man of the people.
Quartet opens on January 1.