Lily Allen, 02 Academy Brixton

It’s girls’ night out. Walk in, the waves of scent and hairspray go right up your nose. And now here’s Lily, sloping on with a half-blonde half-black hairdo like a cross between Nancy Sinatra, an Afghan hound and a very pretty Jimmy Savile. As she crosses the Vegas-style stage, there’s even a touch of Wendy Richard about the high-pitched squeak and bum-wiggling dance. She’s wearing a tiny black sequined number and suggestive seams, and after a lame "Hello London!

Is it Friday night or what?", she apologises because her tights are falling down. But it’s not until halfway through the set that it hits me: Lily Allen is the new Marie Lloyd.

Not that I’ve seen Marie Lloyd live because I think she died in 1922, but if the queen of the London music hall, with all her thigh-slapping innuendo, controversy and personal traumas hasn’t been reborn as this arsey raconteur, I’m a monkey’s uncle.

I'd come with a grudge, having started to find Ms Allen tiring. Publicity is all very well, but why yammer on about other people to get it, hurling hamfisted insults like Frank Spencer with Tourette’s? Apparently low self-esteem is to blame. Being rude is OK because it’s worse for Lily. And then there’s her claim that she’s not a girl’s girl when that’s exactly what she is. What she creates is the music equivalent of intelligent, observational chick lit, giving the distaff point of view in every gory details in a way that has never been done before (or not, at least, since Marie Lloyd).

So I’m doubtful. But then this girl comes onstage with her wig almost slipping off and the way she confesses her mistakes, and it’s impossible not to like her. Take the second song in, "Back to the Start": has anyone ever admitted so much about sibling rivalry, heaped so many ashes on their own head ("It’s my fault, I’m sorry, you did absolutely nothing wrong...") and made such a genuine apology?

But the other thing that makes Allen stand out is her dissection of a world drowning in superficiality, sung so winningly that even people who haven't given the subject much are happily singing the lyrics. "Everyone’s at It" lists the drugs we shove down to get through the day. An imploring throwaway line – ‘Why can’t we all/All just be honest?’ – stands out of the electropop vortex like a plea for a second of sanity. "The Fear" does the same thing, a jingle-jangle headrush indicting everything that’s got us where we are today, from marketing to celebrity culture. Allen has been attacked for presuming to be a social commentator when she isn’t qualified. But what exactly is that qualification?

Compared to this, the confessional stuff is a riot, at least superficially. In the cheery carousel of "Never Gonna Happen", Allen gives her lover the boot in a musically conjured big top where, to comedy drum rolls, oompahs and accordions, she rides bareback while her man sobs like Pagliacci in the sawdust. On the album it’s a bleak black comedy; tonight, the seven vast lampshades hung from the ceiling start going up and down like Monty Python mobiles, adding a sense of surreal madness as Lily coos triumphantly "I! Don’t! Love! You!" She’s presumably between relationships: the single, "Who’d Have Known", gets a jaded introduction: "This is for those couples just starting going out, in the early stages when you... still like each other." Its shimmering pop melody makes it one of the night’s best numbers.

In the second half of the set, we get "Smile" extended into a vicious dub break with rapping from support act Professor Green, then turned into a sexed-up duet involving the SOS Band’s "Just Be Good To Me"; and an astonishing anti-Iraq war song, "Our Bullshit", which she wasn’t allowed to have on her album (surprise), and which she follows by initiating cheers and applause for the British soldiers abroad. We get the Kaiser Chiefs’ "Oh My God", complete with listenable scatting; "Littlest Things", where the off-key notes actually hurt.

And then - unbelievable - she says, "No one’s ever tried to beat me up. Except Cheryl Cole. JOKIN’!" Whatever Lily Allen is – pop star, or pantomime dame – she’s a closet eccentric. And that makes her quite a rare bird.