If one of the UK's finest poets would like a coffee as part of being subjected to an interview, a coffee must be bought.

So Don Paterson - bearded, acclaimed Dundonian poet - and I sit and drink he wryly labels a "hipster Bruntsfield coffee" in the south side of Edinburgh, his home.

We meet in auspicious times. Paterson career as a poet has been laden with awards. He has won the esteemed TS Eliot prize twice, the Whitbread poetry award, the Geoffrey Faber memorial prize, and the Queen's Gold Medal for Poetry.

And now he has just won another. He took the Costa Prize for Poetry for his beautiful book, 40 Sonnets. The judges praised its "cool intelligence and lyric gift". It is the latest of a series of fine, tender, funny, scathing, moving, penetrating books of poetry, including Nil Nil (1993) to Landing Light (2003), as well as his books of aphorisms (The Book of Shadows, 2004, The Blind Eye 2007, Best Thought, Worst Thought, 2008) and several more. Since 1997 he has been poetry editor at Picador Macmillan, teaches at the University of St Andrews and has, in the week we meet, just returned to work on another talent, being a jazz guitarist.

Paterson, born in Dundee in 1963 and raised in the city, should be squarely in the frame to be in the next National Poet, or Makar, now that Liz Lochhead's term is over.

But it is a job he doesn't want. He says: "Not at the moment, to be honest with you...Edwin Morgan and Liz, apart from them being fine poets – they address the issue of Scotland in their work. And both did so brilliantly. And it is important that whoever does that next also takes on that too. It’s a role that comes with certain expectations and it would be crazy to take on that role and just not meet them. So for that reason, personally, I think Kathleen Jamie would be great."

Doesn't that attract, the task of writing about the nation? "Not this week, not at the moment. I’ve got other things that I'm doing. Right now – though you’d be stupid to say never – it would be a distraction from other things. And also you have got to be honest when you see other people who would do the job far better."

40 Sonnets is a rich, profound and justly acclaimed work. It is also, as our literary editor Rosemary Goring pointed out in these pages, full of love: for his sons, Russell and Jamie, for friends alive and dead, for his partner, the writer Nora Chassler, for Dundee, for poetry itself.

Paterson speaks in a low and rather rapid rumble. We talk for a long time - Paterson is funny, self-lacerating, ironic and deeply thoughtful (and entertaining) company. On winning awards, he says: "One thing you never are is blase about it. If I have won anything more recently, I've really felt it has been more for the book. I think that also – I don't whether it is as a recovering Calvinist – I find it harder and harder to take a compliment, because every compliment is like a stab to the chest - so you want to take it as a compliment for the book."

Paterson writes about six poems a year, he says. Completing a book is a "painful process" and it takes, he says, 18 months to recover from.

Paterson wrote a book of sonnets, initially, he says, "which was to get the thing out of my system and never write a sonnet again, because I feel like it has taken too much of my time. " He adds: "I thought it would be interesting to set myself the project of working only within that form. Basically to try and get it down to a motor skill, so I didn't have to think about the form anymore. You nail it like you do a 12 bar blues, or a fugue, and improvise within the form. By the end I felt that the form was becoming pretty invisible and I didn't have to think about it so much anymore."

One of these sonnets, To Dundee City Council, is a pungent blast of invective against the council and its handling of the city's landscape. He says: "And specifically [it was aimed] at the council, not at Dundee. I love Dundee. But I have watched them [the council] – for 52 years – confuse urban regeneration with a post-apocalypse. I just sort of threw my hands up in the air."

He says he is a "St Mary's boy", referring to the council estate on the north of the city being home turf, and still a resonant territory. "Dundee is absolutely part of me. There is something about your childhood territory that is always going to make it your primal imaginative terrain. And there is something about the experiences you had at the most self conscious times of your life, like secondary school, that will always stay with you. All of one's triumphs and great shames take place in front of school assembly in my mind, and always will."

*************

Now Paterson has a new situation. Or should that be, a Don Paterson Situation? That's the name of his new band. Paterson is a jazz guitarist. Paterson moved to London in the mid-1980s to join fellow Dundonian, drummer Ken Hyder’s folk-improv group Talisker. He later formed Lammas with saxophonist Tim Garland and released a series of albums.

But he has not played in a while, as an operation on his hand led to the loss of movement in one finger. "Which for a guitar player is a lot of finger," he notes. "But I got it back, and I contacted Steve Hamilton and I suggested putting something together and we did. It’s kind of ECM-ish Euro jazz, and a lot of it is composed, and there is some Celtic stuff and electronica in there as well". He had its first gig two weeks ago. "I think it went fine. We will be doing it again. "

Music is important to Paterson. "How can I put it? You don’t get to choose what you are better at, and if I had a choice, I would have preferred to be a better musician, really. Because it’s the thing that I love more. Which isn’t to say that I don’t love poetry. But maybe its to say that my relationship with literature has been such a working, professional one for such a long time – inevitably that subtracts a certain amount of the magic."

Does music influence his poetry? "I always think that as a single organism, if you do any two activities, after a while you are going to find analogies and rhymes between them. If you are doing – I don’t know, origami and hang-gliding – it will be the same thing again. A lot of the analogies that people make between music and poetry are actually quite facile, they’re not true. But at a technical level there are some things, in my mind at least, that are mapped to each other." He adds: "There is a normative shift in poetry where sound are sense are much more evenly balanced than they are in other forms of verbal communication. Sound and sense make double-sided signs in poetry, and it helps if you can listen carefully – and I think that’s a skill you can learn from playing."

Playing music and writing poetry differ in at least one respect, he says. "When you are playing jazz, your instrument, in a way, is the thing is that is preventing you playing like a kazoo, which is what you want to do. You have to go through your instrument to do that. And in a sense it is the same in poetry – but it is different in one crucial regard: in jazz you are trying to play what is in your head. In poetry you are not trying to say what is in your head at all, you are trying to figure out what it is that you want to say, or what you don’t know – and use the mechanism of the poem to do so....form in poetry is a kind of investigative, kabbalistic tool for surprising yourself."

Paterson, who is appearing at Stanza, the annual poetry festival in St Andrews on March 4, is also working on other writing. He is writing a play. It may prove controversial. Paterson is writing it with Ms Chassler, and it is, he says, about Jimmy Savile and his crimes. If all goes well, he says, the National Theatre in London will stage it.

He says: "It's actually about one of his victims. It’s about the infantilisation of women and sexualisation of children in the 1970s. But its told from the point of view of one of his victims, who is trying to stage a kind of cathartic panto, in Brighton. I think panto is really an interesting and uniquely British form, where a lot of these terrible power structures are encoded. But Jimmy is kind of a cypher. He is in it, but he is essentially a cypher. Because he was just a psychopath who should have been locked up in Broadmoor."

Paterson adds: "It ties in with the cultural necessity of scapegoats, and those court jester figures, and the role they play for us – as a way of distracting us while other people get away with the same, or far worse. He was an horrific cultural symptom."

He is also writing something more personal, a memoir. He says: "The early years, up to about 20. It’s about growing up in Dundee and playing in clubbie bands and going crazy, ending up in the bin for half a year … a tale of tortured adolescence." He smiles and adds: "As my partner points out – often – I can’t even read a novel, never mind write a novel. I never do well with long pieces of prose. I can’t pay attention or understand why anything takes so long to say."