If fast talking were an Olympic sport, Natalie Haynes would be a gold medallist.

The writer, broadcaster and reviewer speaks at such a rate of knots that she leaves her listener breathless. She has so perfected the art she rarely seems to need to come up for air. Not for nothing is she known as Haynes The Hastener.

The 39-year-old is an erstwhile stand-up comedienne, newspaper columnist and serial judge of book prizes, ranging from the Theakstons Old Peculier Crime Novel Of The Year to the 2013 Man Booker Prize. Today, though, she is sitting down in a London hotel explaining why she stands up for Greek tragedy and the classics. She has just published her first novel, an ambitious Edinburgh-set psychological thriller, The Amber Fury. Inevitably, this noirish book is an homage to all things Hellenic - myths, art and ideas, as well as fate, revenge, violence, obsession and love. Her first book was non-fiction, The Ancient Guide To Modern Life, and she has written a children's book, The Great Escape.

Before we enter the maze of our discussion that twists and turns into many passages about the pleasures of Dorothy L Sayers's Lord Peter Wimsey books, our shared admiration for the historian and classicist Mary Beard, and why Greek tragedy and teenagers are a good mix, we explore why Natalie Haynes is Standing Up For The Classics, the title of her new four-part radio series to be broadcast this month. The programmes, based on biographical material about Petronius, Sophocles, Virgil and a lone woman, Aspasia, have Haynes doing her stand-up schtick intercut with interviews with academics, writers and filmmakers, even singer-songwriter Dido. The series combines Haynes's "two occasional skills, classics and stand-up". Nowadays, she shuns the title.

"It insults people who do that their whole lives. It's a proper job and I don't do it any more... I did not want to spend the rest of my life driving thousands of miles every weekend. I had met my partner (actor Dan Mersh) and we had moved in together four years ago so I retired. I had a wonderful time as a stand-up and it was great to go back to it for the programmes, although performing in front of a Radio 4 audience is not like late-night in the Edinburgh Festival Club. Radio 4 audiences are not going to throw things!"

Which brings us to The Amber Fury, a novel that Birmingham-born-and-bred Haynes suggests should come with a sort of health warning. "Perhaps a sticker on the dust jacket warning, 'Not funny'? I have this fear that people are going to buy it thinking it is going to be full of laughs."

The Amber Fury, told in five acts as in Greek drama, is most definitely not going to have readers laughing out loud since it is about death and bereavement. Indeed, Haynes's depiction of the crippling nature of grief has the harrowing ring of truth. "It really came out of thinking what's the worst thing that can happen to you, a terrible loss of someone you love for no gain to anybody." She tells me the desperately sad, real-life story that made her want to write the book, but asks me not to include it. "I really don't want the people involved to think I am trying to profit from their tragedy, that I have stolen it and made it my own. But the story has stayed in my head for years."

Her protagonist Alex Morrison, a twentysomething theatre director, flees from London to Edinburgh following the violent death of her fiance. She finds a job teaching drama at a Pupil Referral Unit to a group of deeply troubled, recalcitrant teenagers. By introducing them to the blood, guts and vengeance of Greek tragedy she captures their interest and soon the names of Oedipus and Clytemnestra are tripping off their lips. One of her students, who is as isolated and damaged as her teacher, becomes unhealthily obsessed with Alex's private life. The stage is set for tragedy.

The daughter of two teachers, she was 16 when she read her first Greek tragedy, "slowly and badly with a Greek dictionary cracking at the spine". It was Medea - "a hell of a play". Medea, she says, lives in a world of moral absolutes and that is why teenagers and Greek tragedy are the perfect mix. "When else in your life do you perceive things in such absolute terms? When is everything so great, so terrible, so unfair, so perfect, if not when you are 16?" With her father, she then went to see Diana Rigg giving the definitive performance in the title role at London's Almeida Theatre. "I was never the same again," she says.

Unsurprisingly, she went on to read Classics at Christ's College, Cambridge, where "the spectacular trailblazer" Mary Beard was one of her lecturers. After graduating, Haynes ran away to join the circus. "I honestly don't know why I chose stand-up," she says, giving me one of her bright, wide smiles. A surfeit of tragedy? "Maybe, but Classics has been my big USP, not that that's why I read Classics. But it has paid my bills a hundred times over."

Why did she choose the Edinburgh setting? Haynes laughs and then confesses that for a long time the book's working title was Morningside Becomes Electra.

"Too tempting! Seriously, though, I chose Edinburgh because it is the place to go when you are sad - it will look after you. I have lived in Edinburgh and have done 10 festivals and toured there lots of times so I know it well. Also, I went out with someone who lived in Dalkeith for four-and-a-half years.

"I have had two bereavements while in Edinburgh, both of my grandparents. My grandfather died when I was on my way there and I had to turn around and go home. People were so kind. When I was performing at the Pleasance in 2004 and had just come off stage, after a terrific ovation, which did not happen often I can tell you, I got a message to say my grandmother was in hospital. This was before we all had mobile phones, but the Pleasance got me an earlier flight so I could get back to see her - she died a few days later. For me, that is the epitome of Edinburgh: something terrible happens and people say, 'How can we help?' It looks so stern but it is so comforting. It has that glowering thing going on - it is a Jekyll and Hyde of a city. But I have only good memories of it, its facades and its innards, even when performing on the Fringe, which was incredibly stressful - too many comedians!"

After judging so many book prizes - in addition to last year's Booker, she was on the panel for the 2012 Women's Prize For Fiction - is she nervous about putting her first novel out there? A hostage to fortune perhaps, given that she is probably best known as an incisive critic on BBC Two's Review Show?

"Bit of a risk, isn't it? We will have to see," she replies. She was editing her final draft while judging the Women's Fiction Prize for which she read 60 or 70 novels. "Mainly I thought, 'Nobody's book is like mine. Phew!' There was a huge emphasis on historical books and books about both world wars, but there was not that much contemporary fiction so I felt pretty perky at times. Is it as good as the best book I have read? Nothing is as good as the best book you have read."

Last year was a write-off. "I lost all track of time. I read 230 books because I was also judging the 2014 Foreign Fiction Prize. But it was the Booker that ate me! Fifty books in the first 100 days, then 100 books in the second 100 days. It was brutal. I know it's not like going down a mine, I really do, but I never left the house for six months, I had constant mouth ulcers from drinking so much caffeine," she says. "The soft tissue of my body was screaming, 'Go outside. Stop reading.' So many words!"

Nonetheless, she stands by the choice of Eleanor Catton's The Luminaries. And Haynes should know, she has read all 832 pages three times. What's not to love, she asks. "Catton is just a crazy genius."

The Amber Fury is published by Corvus, £12.99. Natalie Haynes is at Aye Write! in Glasgow on April 5. Natalie Haynes Stands Up For The Classics begins on Radio 4 on March 24