`Am I drunk, Prime Minister?'

Harry Enfield is only really funny when he's being someone else. Maybe that's why he got completely hammered at No 10.

Harry Enfield is taking a whole day off from editing his new film - in which teenagers-from-hell Kevin and Perry go on holiday to Ibiza - to plug his new video, Norman Ormal - A Very Political Turtle.

It is now 3.20pm and Harry is flagging. He was up at six to appear on Channel 4's The Big Breakfast, was then whisked off for a photo-call in front of Big Ben, and was subsequently interviewed for Radio 4's Front Row, The Steve Wright Show on Radio 2, and Virgin Radio, before repairing to a handsome suite at the Dorchester where The Independent has an hour- long slot between the Sun and the Express Magazine. The Sun journalist arrived late, sending Harry's PR minders into a spin. But Harry seems unperturbed. Semi-detached, even, which may be the only way to cope with such a nightmarish schedule.

He has a flaccid handshake and three shirt buttons undone, revealing a lot of chest hair, perhaps to compensate for the stuff that has gone missing from his head. I don't know whether he is chippy about encroaching baldness, but he does point out that even though we are the same age (38), I seem to have a much fuller head of hair.

He is a tricky man to interview. He is engaging and funny, which is great when you're talking about doddery old peers, but you wish he would be a little more contemplative when asked about himself. His second child was born earlier this year, but not even the joys of parenthood induce him to give much away. "It's supposed to change your life but it hasn't changed mine really. It's changed [his wife] Lucy's. But I have never slept much." And that is that.

So let's try politics. The Norman Ormal video is a mostly jolly, occasionally savage satire, aimed principally at Tories. It would have been released sooner, but for a sequence in which Enfield, thinly disguised as Jonathan Aitken, admits that he has been lying about who paid his hotel bill, and in a fit of remorse, does "the only honourable thing" - he frogmarches his daughter down to the police station to have her arrested for perjury.

Enfield wondered whether he could get away with this before Aitken was sentenced. "So I consulted my legal people, in the person of Ian Hislop. And Ian said, `no, you can't. You'll go down as well'." He laughs uproariously.

Enfield is an old hand at political satire. His big television break was Spitting Image, for which he provided the voices of David Steel, Douglas Hurd, Geoffrey Howe and Ken Livingstone. More recently, of course, he created the revolting Tory Boy, and was duly considered something of a soulmate by New Labour. That is, until he blotted his copybook by drunkenly abusing Peter Mandelson, then Trade Secretary, at a party at 10 Downing Street. The incident has been well-documented, but I am keen to hear it recalled by Enfield himself.

"I'd written something rude about Mandelson, and he came up to me and said, `What have you got against me in particular?' So I said, `You should resign. You're credited with making Labour popular again, but you're the least popular member of the Cabinet, so by your own logic you should fall on your sword.' He just sort of grinned at me, so I got embarrassed, I thought he'd at least say something joshy. And then I saw Tony Blair, and I went over and said, `You should sack Mandy for the following reasons...' which was when Ben Elton suddenly came between us, and I said to Lucy, `Why has Ben barged in?' and she said, `You're drunk.'

"Well, never tell a drunkard he's drunk. I said, `Lucy says I'm drunk. Am I drunk, Prime Minister?' To which Blair replied [cue his Blair impression], `You know, a lot of people think I'm just the man who stands behind the dispatch box'." Enfield roars with laughter again. "Bit of a conversation- stopper really. I think he was trying to say that he is just an ordinary bloke.

"Anyway, they didn't like me going public on our conversation, which was a bit rich, seeing as the whole point of the thing was for them to go public on their palliness with lots of celebrities." Indeed. And of course, Mandelson did resign. "Yes," says Enfield gleefully, "that's what I would say if I was a politician" - he goes all gruff and posh, and bangs the side of his chair - "I demanded his resignation... and six months later HE WAS GONE!" This time, I laugh uproariously.

Enfield is a hoot, but only when he is pretending to be someone else. I wonder if awareness of this makes him feel slightly insecure? It may even have been why he got hammered at No 10. Heaven knows, he has little cause to feel insecure about his stature in comedy circles. Or to doubt the affection in which he is held by the viewing public. This very morning, he tells me, someone yelled "Loadsamoney!" at him, testament to the popularity of one of his sharpest characters, who even pops up in Hansard: "This is not a `Loadsamoney' economy" - Margaret Thatcher, circa 1989.

But fame has its pitfalls. Enfield still winces on recalling an encounter during a holiday in Cornwall a few years ago, when a passer-by cheerfully referred to another of his characters, saying, "You don't want to go to that beach," and he snapped: "You don't want to be the 1,000th person to say that to me today!" The man's crestfallen face haunted him for months.

Prosperity has its pitfalls, too. Although Enfield is a middle-class boy from Sussex - whose family, as profile-writers have discovered to their joy, were loftily dismissed by Virginia Woolf in her diaries: "I would rather be dead in a field than have tea with the Enfields" - his grandmother and great-uncle were pillars of the Communist Party. And Harry himself used to spoil ballot papers because there were no candidates sufficiently left-wing. Now, of course, he is a self-confessed Bollinger Bolshevik. And while I don't suppose he agonises too much, to paraphrase yet another Enfield character, about being considerably richer than most of us, he is self-conscious enough to make repeated cracks about it. Might the Kevin and Perry film make him big in America? "Oooh yes, that would be lovely. Then I could become IMMENSELY wealthy, and become Lord Enfield of WEALTH."

In a rare moment of introspection, he admits the film is a big gamble for him. But he has to consider new projects, not least because his old muckers Paul Whitehouse and Kathy Burke have declined to appear in any new sketch shows. There hasn't been a falling-out - Burke, after all, plays Kevin's sidekick Perry - but Enfield's relationship with Whitehouse has clearly been affected by the latter's success with The Fast Show.

Significantly, The Fast Show was built around characters Enfield had rejected, such as the "Suits you sir" lecherous menswear assistants. "I still don't see them as funny... I'm not mad about them... they're tiresome, really," he says. "Paul went on about it for about four months, saying `suits you, sir' all the time, with Charlie [Higson, their other collaborator] going `hahahahaha'. I'd say, `I'm going for a pee, and Paul would say `ooh, suits you sir'. And Charlie would go `hahahahaha'. They were encouraging me to like it by stealth. Quite heavy stealth. Stealth bombers. But it put me off more and more." Enfield happily admits to coveting other Fast Show characters, however. "I think Rowley Birkin [the inebriated judge] is fantastic. Entirely up my street. I would definitely have nicked him from Paul."

In the absence of Whitehouse and Higson, Enfield is taking a radical approach with his next sketch show. He signed up with Sky, expressly so that he could exploit the Murdoch empire and invite Sun readers to submit original ideas. He has duly been bombarded with faxes and e-mails. "A 16-year-old from Arbroath has come up with a kid who says `why?' all the time. I like that. And someone else suggested an impatient man in a queue, catchphrase - `I have a wife and child in the car, they are tired and hungry and I want some service NOW!'"

Enfield beams. He is in his element. Giving a performance. Making me, the photographer and his PR minders laugh our socks off. And he pre-empts the obvious question with disarming glee. "Someone else suggested a good character, a cheeky twat who gets Sun readers to do all his work for him." My precious hour is up. Enfield's laughter follows me all the way down the plush Dorchester corridor.