Gascoigne, who was most recently heard of reeling through the streets of Dorset in the aftermath of a three?week gin binge, seems an unlikely addition to its most celebrated denizens.
Then again, he is promoting a film about his life and this, to borrow a ghastly term from the PR industry, is the junket. George Clooney is well versed in this kind of affair, holding court at The Dorchester in a room the size of Luxembourg while the journalist is forced on pain of death not to ask about anything besides the movie being plugged. It appears that Gascoigne is yet to master the same protocols.
Almost immediately, he declares: "I can answer any question you want. Any in the world - I haven't got a problem with it. I took cocaine. I got divorced. I've been in rehab. I fell down in the street drunk. I've had important, famous people ringing me up. I've scored great goals. I've been in car crashes. I can't think of anything else. Well, I haven't banged Miss World."
His face lights up in a luminous, lascivious grin. Clearly, I have caught Gascoigne on one of his better days, one where he is not wallowing in the despair of his alcoholism but revelling in what he perceives as the unhinged hedonism of it all. Burrow deeper, though, and there is a torture behind the candour. Why, I ask, did the concept of making a film appeal. The reply is shot through with self-pity and more than a trace of a persecution complex.
"The fact that I have sued every newspaper meant that I couldn't get my stuff out," he says. "You can't talk to someone when you're suing them. I just wanted to get my point across about what it's like to live the life of Paul Gascoigne. How many lies have been written about me, about the things that have happened to me and what I sometimes put myself through? People need to realise that I am human. I'm not some superhero. Don't think that everything said about me passes over my head, because it doesn't.
"Some of it, I have had to take on the chin and get through it. Other things I did to myself weren't good, but in England, it's great becoming famous and then as soon as you're famous they knock you down. They do it to everybody. And I have had to cope with a hell of a lot in my life."
That last statement is true enough. There has been the tempestuous relationship with former wife Sheryl, the notorious 'dentist's chair' episode with his England team?mates in Hong Kong, the spell in The Priory after downing 32 shots of whisky, not to mention the night in 2010 when he decided to furnish his 'friend' Raoul Moat, a homicidal fugitive, with a chicken dinner and a can of lager. "I just wanted to say, 'Come on Moaty, it's Gazza'," he explained then.
Gascoigne's has been an existence of epic indulgence and endless precariousness. One would imagine that no big-screen treatment could do it justice, and director Jane Preston's tender biopic does not attempt to. It luxuriates in his innate talent with a football, best freeze?framed by his sumptuous goal for England against Scotland at Euro '96, but excises much of the dark epilogue to his career. A document of his wanton road to ruin is sacrificed in favour of a fond celebration of his more absurd escapades, not least the time he took an ostrich with him to a Tottenham training session.
Surely, a personality like Gascoigne - eager to be caricatured as lovable rogue, but pathologically anxious about intimations of anything more sinister - must be delighted at the film's depiction. "I haven't seen it," he says. Given that he is sitting alongside a giant poster for the thing, this comes as a fairly startling acknowledgement. "No, I don't need to, because I did it."
Gascoigne gives off the air of a man who believes he is unfairly traduced. "There was the bulimia, the obsessive-compulsive disorder, and I had to conquer all that," he argues. "To conquer fear, you have to face it. There have been a lot of demons in my life, but I got through them all.
"Sometimes, journalists won't give you a chance. Every time I moved up a level and felt back to myself, I got knocked down again. It has happened so often, and a guy can only take so much.
"I know I'm famous, but I don't act in the way of being famous. I'm just a normal guy, trying to live as normal a life as possible. I deal with things as best I can, but it's the lies people print that can follow me all over the place."
If you are starting to suspect that Gascoigne is a touch paranoid, you would be right. At 48, Gazza is apparently so terrified by the idea of his name being in the news that he claims to have a panic attack every time he sees a headline about the Gaza Strip. His obsession with counter-surveillance, amid fears that his mobile phone was being hacked by tabloid newspapers, became so acute that his family had him sectioned.
Gascoigne won more than pounds 188,000 in damages last month, after he was found to have been the victim of sustained press intrusion.
But it is clear, when he is asked whether he feels he has turned a corner, that the sense of foreboding endures. "What's turning a corner?" he shoots back. "I have been hacked for 21 years, by every authority. It might be the police who hacked my phone and handed over information to the press. You are supposed to ask a policeman for help and then you find out you are getting hacked by one. Who do I turn to?"
I suggest that it can be very difficult to gauge what precisely is happening in his world, when he is pictured blind drunk one minute and then flatly denies it the next. At which point the victimhood kicks in again. "I'm in the countryside for three months, chilling out with my ex-wife, and in that time I'm meant to be injecting my groin with heroin, falling off a pier in Bournemouth, and falling over in a nightclub. And yet I'm sitting in my house.
"It's horrendous. Not long ago, I was sitting with two lawyers, saying, 'Look, what are we going to about these lies? We've got to sue them.' They said to me, 'You can do it, Paul.' Do what? I've been sober for a year-and-a-half, what do you want me to do?"
Gascoigne has endured so much self-induced anguish, ever since he was sacked from his last gainful employment as Kettering manager in 2005, that it can be hard to pick out a low point. But he is unambiguous, reflecting upon one episode so grim that he refers to it as his own death.
"Nearly three years ago, I died in America. I was in rehab for two days and on the third day, I couldn't stop the shakes in my hand. I was having my heart injected constantly to keep me alive. I remember saying to the doctors, 'Please don't let me die.'
"They put me to sleep for 18 days, I was so far gone with shaking. I woke up, asking, 'Where am I?' That was the scariest point. They couldn't detox me and the only way they could keep me alive was to inject my heart and lungs. Everything after that is a relief. I knew that I couldn't mess about with it any more.
"When I was drinking, I didn't think of that. I was just enjoying myself. But there's nothing worse than becoming sad and then starting to drink on it. I was never depressed, though, that's just an excuse. I was just miserable drinking. I isolated myself, and I shouldn't do that, because I know that I have a lot to give people - and that others have a lot to give me."
It should be time, at last, for him to heed the wisdom of that sentiment. Gascoigne - brilliant footballer, feckless boozer and now, implausibly, film star - is belatedly preparing to step back from the precipice.
