That winning, very British sense of embarrassment is Evans all over. Whether spectactularly failing to get the girl in There's Something About Mary or accidently-on-purpose walking into the mic-stand on stage, his whole persona is based on nervy, yet charming incompetence. He might as well have "LOSER" branded on his forehead. He has turned the (deliberate) cock-up into an artform. His schtick is that he'd rather be anywhere than up there performing in front of thousands of punters. In conversation he refers to himself as "an idiot."
And that's why people warm to him. They can identify with his portrayal of a person constantly at two with the world - the man who disastrously misuses a French "hole in the ground" lavatory or who is baffled by hotels: "I opened the wardrobe and there was a pillow and a blanket. That was the worst night's sleep I've ever had." He closed his recent show at the Montreal Comedy Festival with a song about how he messed up a suicide attempt: "I tried cutting my wrists. I tried, but I missed." Failure has made Evans a roaring success.
He now has the pulling-power - matched in comedy by perhaps only Eddie Izzard and Billy Connolly - to fill a London West End theatre for 10 weeks. That is to say nothing of a burgeoning movie career which includes the acclaimed tale of fading end-of-the-pier performers, Funny Bones, the zany box-office hit comedy, Mouse Hunt, and the culty futuristic Luc Besson picture, The Fifth Element.
In There's Something About Mary, Evans tones down his clowning to deliver an impressive performance as a tweedy English academic who is trying to woo the delectable Diaz. Made by the wonderfully daft Farrelly Brothers (responsible for Dumb and Dumber and King Pin), this is a film that taste forgot. I won't tell you what happens when one of the characters zips up his flies too quickly - you might be eating. But if you're prepared to check in your PC sensibilities at the cloakroom, you'll find Mary a belly-laughs, no-brainer romp. It's also a showcase for Evans's growing talents as a character actor.
He went down a storm in Montreal, too. He puts so much into every show you almost fear for his health. You look on in awe as he hurls himself into acting out everything from a drunk trying to urinate to the last item of luggage left on the carousel: "Don't leave me here, I don't know anybody." Towelling himself down on stage, he remarked at one point: "If I went to the toilet now, I'd pass steam."
At the curtain-call, the whole front row insisted on shaking his hand: "What I'd like to do now is shag you all," he exulted. But as soon as the show was over, he dashed for the haven of his dressing-room and just sat there quietly with his shirt off, cascading sweat and puffing out his cheeks.
The next day was less frantic. Dressed in a crisp white shirt and blue jeans, Evans unwound by improvising some show-tunes on the grand piano in the corner of a conference-room at the hotel. A bit later, putting his feet up on the sofa, he shook his head and said: "I'm just not built for schmoozing. In England, we're brought up to think 'don't get too big for your boots'. We prize modesty. I'd never fly into Heathrow and say, 'Out of my way, don't you know who I am?' They'd fill you in on the spot in Immigration. They wouldn't stamp your passport, they'd stamp your chin."
Evans, now in his mid thirties, has always been spurred by a desire to prove himself. In the late 1970s, after school in Southend (where he still lives with his wife and young daughter), he followed his musician father onto the working men's club circuit. He admits that his innovative comedy was not always a hit with audiences expecting mother-in-law gags. "That's when I started doing physical comedy, because then you're like a moving target."
On one notorious occasion he didn't move fast enough. "I was beaten up in Cardiff. These six guys tried to steal me car after the show because I was so bad. But the steering lock was on so it just went round in circles."
For a while in the mid 1980s, Evans was a comedian in search of an audience. "I was wearing a glittery suit and performing on a circuit where everyone was doing traditional stuff: 'The wife's fat' - the wife was always fat. I remember doing the West Ham Working Men's Club one night and I died on me arse. Someone said to me afterwards, 'What you're doing isn't going to work here, but there is a place where it will - the Comedy Store.' At last I'd found somewhere you were allowed to say what you liked, rather than all that racist, sexist crap they wanted in working men's clubs." An appearance on Friday Night Live soon followed, and Evans never had to worry about lairy punters in car parks again.
For all that, he still manifests what psychologists would no doubt label Classic Neurotic Comedian's Syndrome: he's a man who can't quite believe his own popularity. "I'm motivated by fear of failure. It's a personal mission to say to all those people from years ago, 'Look, I'm seriously not a failure.'
"Stand-up is therapy. I'm sure every comedian has something wrong with them. The Montreal Comedy Festival is just a massive therapy session. Every day you get bouts of depression and think it's not working. If it's going well, you go, 'Yeah? Why?' You're never pleased. That's why you're a comedian."
It would be wrong to get the impression from all this that Evans is a morose, depressive, Hancock-esque figure. Hitting you with a devastating right-left combination of patter and gags, this former boxer makes for invigorating company. He's just driven - as all the best performers are - by a nagging sense of insecurity and a restless urge to improve.
He isn't, for instance, relishing the prospect of a West End run: "It fills your pants, but you've got to keep challenging yourself." That's one reason why he is keen to develop his acting; he's reading up to a dozen scripts a month.
"It's best to have a few strings to your bow. That's what Mel Smith, Griff Rhys Jones and Rik Mayall have all done. I wouldn't want to be one of those 50-year-old guys still going 'Wa-hey' and dancing on pianos in a crappy suit and a shirt with big collars - 'Well, he was all right till he fell down and couldn't get back up again.' It's not a very good gig when the audience have to rush on stage to help you up." That gig is some way off, you feel.
Edinburgh Playhouse (0131 557 2590), 4 & 5 Sept; Apollo, W1 (0171 494 5586), 14 Sept-21 Nov. There's Something About Mary is released on 25 Sept.