WHEN I tell my wife I'm interviewing John Byrne she asks if I'm going to try to "outdress" him.

I'd be lying if I said I'd given the matter no thought. But hearing the ever-so-slight note of caution in her voice, I realise how futile it would be to try. In this case, discretion is the better part of taking on Scotland's most stylish man in a sartorial arms race. "No," I reply. "You can't outdress John Byrne."

The proof comes sauntering through the door of an Edinburgh gallery a couple of hours later as the 75-year-old fills the tall, echoing rooms of the Fine Art Society on Dundas Street with a gravel-voiced "hello". He's resplendent today in a royal blue suit and tan brogues, with a white shirt peeping over the collar of his brown jumper just so. In his top pocket is a gold-coloured silk handkerchief and what looks like a pair of sunglasses. The day is dreich as hell. I can't not compliment the man. He laughs, then shows me a frayed bit on the jacket near the buttonhole. "That's a rabbit," he says. "A house rabbit". The leporine assailant even has a name: Thistle. "A total sweetheart," he adds. And, somewhere within that famously bushy beard, he grins.

Byrne's charm and apparently effortless style certainly leave an impression. But a more quantifiable legacy is the mountain of art he has produced since leaving Glasgow School of Art in 1963, and the sea of words which, for over three decades now, he has set lapping at the feet of Scottish theatregoers (and, too rarely, their couch-bound, telly-watching cousins).

In the list of recent Scottish cultural landmarks his 1978 play The Slab Boys and 1987 TV series Tutti Frutti sit alongside the likes of Trainspotting, Black Watch, Lanark and The Cheviot, The Stag And The Black Black Oil. And, though he's yet to have a full Scottish National Gallery retrospective like the one bestowed on John Bellany in 2012, he had a major show at the Scottish National Portrait Gallery (SNPG) last summer which included his iconic studies of Billy Connolly, Robbie Coltrane and former partner and muse Tilda Swinton.

Byrne accompanied the 2014 SNPG show with an exhibition of work here at the Fine Art Society. It was called Dead End. His new show, which opens at the Fine Art Society's main London gallery next month, is called A Matter Of Life And Death. Both titles come from films, the first a hard-boiled 1937 gangster flick with Humphrey Bogart as a hood called Baby Face, the second a wartime Powell and Pressburger classic starring David Niven as a stricken airman who somehow cheats the afterlife.

Both, you will note, feature the D-word in their titles and the paintings themselves are equally unambiguous: Byrne's newest works are dark, threatening, sometimes murderous and peopled by men and women in 1950s garb being harried by alarming-looking black cats or elongated skeletons. One painting shows a man fallen in the shadow of a blasted tree as one of these bony actors looks on from the topmost branches. And if you haven't quite got the message yet, the title does the rest. The painting is called The Traveller - Destination Unknown. These, then, are meditations on mortality. Yes?

"I think they must be," he says cheerfully. "I don't interpret them, but they come from my unconscious and my unconscious is, not obsessed exactly, but it has to dawn on you at some point in your life that you're going to die. But it's not an unhappy occasion at all. It would be nice to welcome it when it does come."

As for what comes afterwards: "You either think there's going to be a black hole, or there's some sort of afterlife or redemption. Nobody asked to be put in this earth and we have lots and lots of ways of using our time. I really enjoy working and doing something that's inventive and feeds me, feeds my soul. And it wouldn't matter if people saw the stuff or not. To a degree I would still do it. I hate being idle. To me that's facing life and death, being occupied."

And what does he think awaits him: black hole or afterlife, either the Powell and Pressburger version or the more traditional sort?

"I get dubious on certain days," he says. "Dubious days [are] when I think there's nothing else, in which case what are we all worried about if there's just unconsciousness?"

That indicates a faith then, I say. He nods. "It's not fashionable at all. It's been constant throughout my life because I was brought up a Catholic and I go now to St Peter's which is just along the road. I've forgotten all the responses to the Mass so as a cover I strum my guitar in the band at the back of the church."

Byrne isn't exactly returning to a church he left, nor has he discovered a faith he didn't previously have. But over the last few years he has had another sort of conversion: to narrative painting - like faith, a deeply unfashionable pastime. "I despised narrative painting, thought it was just so old-fashioned and indulgent," he says. "But now I love it."

He's also working harder and (he says) better than ever before, painting 14 hours a day, seven days a week in his small Edinburgh studio. "This is the most fertile period of my entire life. I just feel as if I'm coming into my own now and there is a new energy and vitality about my stuff."

And why is that? "My life is much more serene. I'm less worldly ambitious than you have to be to make anything of yourself when you're younger and want to make your mark on the world at all costs. I care less about that now."

That wasn't always the case, of course. Born in Paisley in 1940, Byrne's desire to make his mark was consuming, at least if we view the hopes and aspirations of The Slab Boys' Phil McCann as an expression of Byrne's own feelings at the time he was working in the "slab room" of a Paisley carpet manufacturer. Unlike McCann, he made it to art school, graduating as a prizewinner in 1963.

Throughout the late 1960s and early 1970s, Byrne painted and made a living in London, illustrating covers for books and records. He did sleeves for albums by Gerry Rafferty and Donovan and a design originally commissioned for what would become The Beatles' White Album eventually saw the light of day on a 1980 release, The Beatles Ballads.

In 1972 he designed the set for Billy Connolly's The Great Northern Welly Boot Show and his much-loved 1974 portrait of Billy Connolly is now owned by Glasgow museums. You can see an equally well-known self-portrait from the same period in the Scottish National Portrait Gallery. It shows the artist sitting on a suitcase holding an easel.

As that decade turned, Byrne immersed himself more fully in theatre by following The Slab Boys with two more plays featuring the same characters. He also wrote a handful of radio plays and then Tutti Frutti, which screened on television in 1987 and brought his old friend Robbie Coltrane to national prominence. Three years later came Your Cheatin' Heart, which starred Tilda Swinton and marked the start of his relationship with her. (By happy coincidence, the long-overlooked series finally comes to DVD this week, a fact Bryne asks me to point out in one of several texts he sends me the day after our interview. "PS Advertising blurb," the message begins. "Your Cheatin' Heart out on DVD on 25th May only 25 years after being shown on BBC").

Within a year of leaving art school, Byrne was also a husband and a father, having married fellow art student Alice Simpson in April 1964. His son, John, was born in the same year and a daughter, Celie, followed in 1965. Was he a good parent?

"No. I was a terrible parent because I had to make my mark. I was ambitious. I wrote Tutti Frutti and Your Cheatin' Heart while they were teenagers. I was virtually an absentee father. I was always working. Having made the mistake the first time of not being hands-on at all, I was more hands-on with the twins."

The twins are Honor and Xavier, born in 1997 and Byrne's children with Tilda Swinton. They're now in their final year at school in Forres, near to the house in Nairn the family moved to from London in the early noughties. Byrne's relationship with Swinton ended around 2006, however. Later there were lurid rumours about a menage a trois involving her new partner - rumours that Byrne has repeatedly and convincingly rebutted. His current partner is Jeanine Davies, a theatrical lighting designer. The couple live together in Edinburgh.

It must have been a real wrench to leave Nairn - and the twins? "It was difficult. Yeah. But it hasn't affected my relationship."

And how's his relationship with Swinton? "Very good," he says.

On his relationship with the art world he has much more to say, and here he has criticisms to air and grievances to voice. I ask him about widely reported comments he made earlier this year in which he's said to have called Glasgow School of Art a "fun factory" and "a third-rate night school" turning out students who can't draw and whose only aim is to win celebrity through the medium of the Turner Prize. He later clarified those comments, saying he had been misquoted. But still he criticised what he saw as a lack of camaraderie, generosity and craft at the school. I ask him what he meant by that.

"They split the studios up into wee sheds where you can sit on your own with your laptop," he says. "It subverts the architect's wish to design somewhere where everybody works together and there's some sort of camaraderie and exchange of views."

The art produced, he thinks, is disconnected from the public, a malaise he also sees in the wider art world. "Everything's about infantilism," he says. "Look at Jeff Koons: the flower puppy, Popeye. It's infantilisation."

He's prepared to talk politics now too. Ahead of the referendum, Byrne didn't voice an opinion either way. "I didn't want to," he says simply. But in the wake of the General Election and the SNP's overwhelming victory in Scotland, he will speak. So where does he think the country is headed?

"It's in a good position at the moment," he says. "And the best position will be when it's like the Republic of Ireland and is independent."

So he is pro-independence? "It would be nice," is all he'll say, which doesn't quite answer the question. "See, I'm an Anglophile. But if we could be like Ireland ..."

Byrne is open enough about his art and his political views, but he's a little more cagey about his current writing project. He will say it's a stage musical, that he wrote what's known as "the book" some time ago and is currently in negotiations with a potential producer. "It was an idea that had been brought to me and I did it and then it sat. I wrote it in Nairn so that was a good 10 years ago. There's a possibility it will come to fruition," he says.

We end more or less where we began, with Byrne's assertion that he's now working harder and better than he ever has before and a discussion about why that might be. And this late flowering is literal as well as metaphorical: included in A Matter Of Life And Death are three paintings of flowers, his first such studies if you don't count the ones with which he decorates on his numerous guitars.

One reason for the productivity, I suppose, is the knowledge that time is running out. Byrne once said that he didn't want to get to the end of his life and find himself moaning about all the painting he didn't do. But another reason is a lesson he learned when he destroyed a body of work made in anger a little over a decade ago: that he needs detachment and order if he's to paint well, and make work that's significant.

The anger was a result of discovering in 2002 that his mother had been sexually abused by her father over a considerable number of years, from the age of about 16. Tempering the anger was a relief of sorts that he could finally discern a reason for the schizophrenia which had afflicted her. Until then he had worried the condition might be hereditary.

I ask him if that belief had ever coloured his work. After all, he did once have an artistic alter ego called Patrick, also the name of his maternal grandfather.

"I think it probably did, either consciously or unconsciously," he says. "Then I discovered the truth about why she had been ill. Shocked is the wrong word. I wasnae surprised. All the bits made sense. Everything made sense and fell into place, which was a good thing to happen."

Thinking back, he remembers the day his mother found out her father had died. The family didn't have a phone so the news came in person from Byrne's uncle. His mother went to pieces. "I've never seen anybody so out of their mind with grief," he says. Then he tells me about a family photograph he had showing his mother at 15. "She was radiant and wearing a sailor suit and hadn't a care in the world. And it happened just after that."

I point out that he often used to paint people in sailor suits. Nautical wear even features in Donald & Benoit, the children's book he wrote based on characters created for Honor and Xavier's night time stories.

"Yes," he says. Then, after a pause: "I hadn't made that connection."

On the back of that dark family revelation he made a body of work that he now says was "terrible", "dreadful", "incoherent". It was "a roar of rage about how much I had hated that man. But it wasn't true. I loved my grandfather and I still do to this day".

But the experience taught him something vital. "You need to be detached to make great work, with impact. I don't mean peace of mind, but you cannae be all over the place. You have to be ordered, which is why my work is so much better now - with that detachment and with that knowledge."

Outside the gallery the rain has stopped, the leaden sky has turned a deathless blue and Byrne ambles off to enjoy the cigarette he's been patiently rolling as we've talked. I imagine he'll slouch stylishly outside, like a corner boy in one of his own paintings. And if those are shades in his top pocket, maybe he'll pop 'em on, just to complete the look: a wise old cat, worried at by rabbits and a little careworn, but enjoying his time in the sun.

A Matter Of Life And Death opens at the Fine Art Society, London on June 3 (until June 25). Your Cheatin' Heart is released tomorrow (Second Sight, £19.99)