Admiring the London skyline from his publisher's impressive offices, Graham Norton looks tanned, trim, and ready to resume work after a long summer break.

As well as being the most popular chat-show host in the country and one of the nation's favourite 'agony uncles', he's now ingratiating himself with the UK's literary glitterati, having just penned his second novel, A Keeper, following the bestselling success of his first, Holding.

"What's been incredibly surprising to me is how willing other writers have been to welcome me into the fold," Norton reveals. "I thought there would be a bit of, 'Oi! Clear off! Go and do your chat show!' But actually, they've been incredibly welcoming."

He's now on the circuit of book festivals and industry events and is delighted that other top Irish writers, including Marian Keyes and John Boyne, have been very complimentary about his latest novel. "If a novelist started a new chat show, I don't think I'd be as nice," he observes wryly.

It seems everything Norton touches turns to gold. He is the third highest paid BBC on-air star behind Gary Lineker and Chris Evans, and his pay-packet has been well scrutinised over the last few years.

Evans is leaving Radio 2 for Virgin, and BBC Director General Tony Hall recently said that his pay revelation was a factor in his exit. Norton, however, has no intention of jumping ship at the moment, despite the attention his own salary has attracted - but he concedes that he doesn't think he's worth what he earns.

"If I was my agent, I wouldn't be earning what I earn - but that's why I have an agent. I don't feel I have to defend it.

"When I heard it was going to be happening (his pay revealed), part of me thought, 'Oh, I should just walk away from this', but actually when it happens, it's just news for a day and then it's gone – you just get on with your life.

"If you were going to do your last hoorah, maybe you'd go to Sky and take Murdoch's millions and then go sit by the beach for the rest of your life, but I don't imagine I'll do that."

For now, the eight-time Bafta-winner is happy to carry on presenting his popular Friday-night chat show and Saturday morning Radio 2 show – alongside his agony column in the Telegraph and, of course, writing novels, having already penned two memoirs as well.

The latest fiction sees female protagonist Elizabeth Keane returning from New York to her childhood village in Ireland, following the death of her mother. Once back, she discovers a bundle of letters sparking questions about her paternity, the father she never knew and the secrets her mother never told.

The story is told in two timelines: Then (40 years previously, telling the story of her mother and how she first met her father); and now, as she juggles her own complicated life with an ex-husband and teenage son.

Norton, 55, could have taken some of the storylines from his own agony columns, as he weaves lonely hearts, contemporary single parenthood, suicide, mental health issues and fractured relationships into the tale. At times, it's quite dark.

"We all have dark times. Maybe it's because I'm Irish but, for me, dark times are private times. I might talk to friends but I'm not going to write a newspaper column about it."

While his storylines aren't actually from his agony column, he can see the connection, and notes: "What's interesting about the agony column is people's resilience and what people can cope with - and I always find that inspiring."

Radio 2 listeners will hear Norton and fellow comedian Maria McErlane mull over readers' letters on his Saturday morning agony slot, often taking different standpoints on issues, and there is much laughter on the show.

"Sometimes we go over the edge," Norton admits. "It all depends on what the problem is. Sometimes the problems are just stupid so you can ridicule people, but if it's a real problem and you feel that people have actually properly written in for our help, then you have to be respectful.

"We've had such sad things. We had woman with a terminal illness who wanted to know about building memories with her children. Maria and I just ended up sobbing through that."

He laughs loudly when asked if he takes himself seriously as an agony columnist.

"I don't have qualifications. I'm 55, I've been around the block and I take the Telegraph column seriously because there's a duty of care there. In one letter out of three, I would suggest that people do talk to a proper counsellor or consult a doctor. I still stick my oar in but then I'm covered."

The novel comes out at the same time as a new season of his chat show, and he confesses there are guests he'd still like to welcome onto the sofa for the first time.

"Angelina (Jolie) is always welcome, so is Brad (Pitt), even though they're not together any more. We still have never had Julia Roberts, as far as I know, but these conversations always make me nervous as I think, 'What if we have had them on but I've forgotten?'"

He feels celebrities tend to be more careful about what they say these days, for fear of their words and actions going viral.

"Television used to be so disposable. The show went out on a Friday night, you either saw it or didn't see it. Now these clips go around the world. I feel sorry for people like Jennifer Lawrence. It seems like every time she comes on, she ends up having to apologise for something – and it's always nonsense. She's so lovely and such good fun.

"People become more reluctant if they've got a funny skill. Say for instance, they can juggle. If in the past we found out they could juggle, we'd ask them to juggle and they would. Now, they think if they juggle on this, they'll have to juggle on every show they go on for the rest of their life. So they decline."

Away from the TV and radio studios, Norton lives happily in London with his two dogs, and although he could afford to retire, he doesn't want to.

"You see friends who don't work and they go a bit Billy bonkers. They over-analyse everything and become involved in the minutiae of their lives. It's not very healthy," he reflects. "I just want to carry on while I'm still having fun."

A Keeper by Graham Norton is published by Hodder & Stoughton on October 4, priced £20.