The four-months pregnant GMTV presenter sighs heavily as Draper points out in his blunt fashion that the birth of their second baby – they have a three-year-old daughter, Darcey – is due in August. (The gender is yet to be determined, although Garraway constantly refers to the baby as she.)
"End of July, beginning of August," interjects Garraway. "Yeah, well, it better not overshadow my birthday, which is August 15," he responds.
"So we'll be employing all the tricks of the trade – lots of curries and lots of sex, which is what we did last time round. In fact, why not begin now and get a head start?" he leers at his wife.
"This is what he's like," says Garraway, "I spend my whole life raising my eyes to heaven."
She also seems to spend a great deal of her time laughing with and at her 41-year-old husband, the son of a Scottish mother and an English father. Despite his marriage to the glamorous broadcaster, Draper is, of course, doomed to be remembered as the New Labour lobbyist who told an undercover Sunday newspaper reporter in 1998 that he could sell political access for cash: "There are 17 people who count (in this government]. And to say I am intimate with every one of them is the understatement of the century."
The legacy of those words means that Draper's name is still, more than a decade later, regularly preceded by the description "disgraced". He has certainly lived to regret those boasts and will do so until his dying day, he says. "I'm ashamed of what I did and I have to live with that shame," he says when I meet him and Garraway at London's Groucho Club.
But that's Draper for you, or if you prefer, Dolly or Muttley (to Peter Mandelson's Dick Dastardly), just a few of the sobriquets under which he used to appear in the red-top gossip columns in the days when he was a flash man-about-town and Mandelson's bag man to boot. Indeed, both Dolly and his wife – she likes "the Lady and the Scamp" label someone pinned on them – admit that this likely lad from working-class Chorley, in Lancashire, still hasn't learnt to button it, even after reinventing himself as a psychotherapist and author.
Whereas the most shocking thing that has ever been revealed about Oxfordshire-born Garraway – "her family's middle-class," Draper points out – is the fact that last May she admitted to lying about her age – by all of one year – and was turning 41, not 40. And, of course, she was a sensation when she took part in Strictly Come Dancing in 2007.
Her comic lack of rhythm and two left feet endeared her to the nation as she was voted back week after week, while the judges fumed over her perverse popularity. (One Sunday newspaper's false allegation early in 2008 of an affair with her dance partner, Anton du Beke, resulted in more headlines and a six-figure libel settlement. It was Draper, not Garraway, who broke down in tears when the apology for libel was delivered in court.)
Nonetheless, Garraway is married to a man who gives off a distinct whiff of danger – they have revealed in various newspaper columns that they have blazing rows, mainly about her untidiness and his inability to put down the lavatory seat. When the Guardian profiled Draper last July as he returned to the Labour fold as a part-time unpaid campaign adviser – launching a new website, LabourList.org – the Edinburgh-born Tory MP Michael Gove compared him to a character in a novel, "because you don't know what he is going to do next".
So, is he as Machiavellian as he's been painted? His wife is constantly portrayed as his polar opposite – uncomplicated, artless and guilelessly charming, even when pretending to nuzzle a calf to publicise her Channel 4 documentary, Other People's Breast Milk, in August last year.
"Machiavellian, me? Nah!" snorts Draper. "After all my years in politics I've been around some incredibly Machiavellian people, I can tell you – and I can't begin to compete with some of them."
Would he care to name names? Baron Mandelson, perhaps? "Actually, no. With Peter, I promise you, what you see is what you get."
"Just like you, darling," purrs Garraway, adding that if Draper were a Machiavellian, then he would be much more practised at the golden art of putting up and shutting up. "And you're not. A true Machiavellian would use silence. You always speak out," she says. The unsaid "unfortunately" hangs in the air as she nibbles on a chocolate chip cookie, her remedy to cope with the morning sickness that has plagued her second pregnancy. If she didn't eat all the time, she'd have to keep getting up off the GMTV sofa to throw up, "which would not be very attractive at all".
Sofas bring us to another well-upholstered item of furniture – the analyst's couch, since we're here to talk about Draper's new self-help book, Life Support: A Survival Guide for the Modern Soul, in which he puts himself on the couch while offering words of wisdom about the root causes of unhappiness. There's also candid advice on how to break free from them, much of it gleaned from his private psychotherapy practice in Marylebone, London, as well as his work on depression for which he has won an award from the mental health charity, MIND.
Draper has fictionalised case studies to preserve patients' confidentiality, but he certainly doesn't spare himself. He writes with frankness and honesty about his own dark nights of the soul, quoting the novelist Tom Wolfe's phrase "Masters of the Universe", from Bonfire of the Vanities, to describe men who are outwardly strong and successful.
"I was a junior version of such a phenomenon when I worked in politics," he says, adding that he was also unfaithful to every one of his many girlfriends. "I left a trail of destruction behind me, in terms of let-down friends and broken relationships.
"For me, my early involvement in politics gave my life meaning. But eventually those elements fell away. First, I felt I lost my soul, then my work didn't come naturally any more. It began to feel alien. Then I ceased to be able to work and lost my energy, eventually breaking down and becoming profoundly depressed," he reveals.
"Everyone assumes I got depressed because of the scandal. Actually, I had been depressed for two years, from around 1996. I thought I had a physical virus. I'd always been quite arrogant and cocky, but I think I put all my unhappiness into my obsession with the Labour Party."
He pauses to drink his tea and then says: "The really spectacular breakdown came two years into my depression with the lobbying thing. That was the killer and I was admitted to the Priory; then I started to get better. I am over it now, though. I haven't been depressed for years, since just before I met Kate, who has changed me for the better anyway.
"I got rid of my depression by doing a lot of intensive therapy, taking the prescribed anti-depressants, doing yoga and finding solace in prayer, because I eventually realised I had been masking the depression for years with overwork, drinking or womanising."
It was a long time, however, before he realised that his obsession with work and politics "and the power-playing that went with it, and the drink, drugs and promiscuity, were all toys and inside, unbeknownst to me, the little child part of me was in the driving seat".
So, despite the serial shagging, the coke-snorting and being the man who put the party into Party politics, he was just a little boy lost?
"I guess. Far from being the Master of the Universe I was more like the tyrant in the playroom. It was only when I reconnected to the child part of me, and was able to offer him the love and stability he craved, that he began to calm down, and my life began to settle."
As a practising psychotherapist Draper is still in therapy and is a Christian, regularly worshipping at his local Anglican church after a flirtation with Buddhism. "The point is that therapists are always working on themselves, just as much as they are helping their patients to work on themselves.
"Hopefully, it will make me not only a better therapist but a better husband and a better father," he remarks. "We are healers, not heroes."
He is regularly counselled by the renowned therapist and author Susie Orbach – famously Princess Diana's therapist – who also seems to be a bit of a heroine to Draper, who says he feels more like someone at the start of his life, as opposed to halfway through it.
He is, he insists, a changed man in every way. The old Derek is no more".
"This is the new Derek," he says, grinning, although clearly the hairline is receding, the waistline is thickening. He is, he notes, with some sorrow, often described on the internet as "a fat bastard", although that's far from the worst thing that's been said about him, particularly by online political blogger Guido Fawkes, who regularly taunts the "new" Dolly.
Perhaps, though, the "new" Derek also owes a debt of thanks to the matchmaking abilities of his and Garraway's mutual friend, GMTV's political editor Gloria De Piero, who first got the couple together.
For him it was love at first sight, although he'd assumed that as a morning TV anchorwoman Garraway would be a blonde airhead.
I remember saying to Gloria, "As if I'd want to go out with someone from breakfast telly!' I bought the stereotype – high maintenance bimbo only interested in glitz and glamour."
Garraway: "Like Andrew Castle? Only joking! Gloria had told me I'd like him because he was really clever and lots of fun. And he was – in a really good way."
Draper: "She claims that she didn't kiss me on the first date."
"I didn't!" explodes Garraway.
"You came back to my flat and had a cup of tea, then I got you a taxi and gave you a hug," he replies.
"This is exactly another description I'd been given of him – the overweening arrogance," says Garraway, with a wide grin, eyes rolling to the back of her head, adding that on their first real date he took her to an exhibition of amateur watercolours at his local Anglican church. "I thought this must be some kind of test. It was the least glamorous invite I'd ever had. It was really rather sweet."
"We went for a pizza – and that was it," declares Draper. Their wedding and the arrival of Darcey were both covered by OK! – and they will sell a photo spread of the new baby to the magazine, because, says Garraway, they can control the images. The money will go into a bank account they set up for charities they both support, such as Help the Aged and MIND.
Does Garraway think she would have wanted to date the "old" Derek? "I don't know because I've definitely only ever known the new Derek."
Draper: "I always say she may find the new Derek nicer, but she'd have fancied the old Derek more." Cue more eye-rolling from Garraway.
Life Support: A Survival Guide for the Modern Soul by Derek Draper is published by Hay House, priced 8.99.