Lily Allen @ Somerset House, July 17

Say what you want about Lily Allen, the girl knows her fans. Tonight’s gig – part of the ten-show Summer Series at London’s historic Somerset House– is a master-class in how to capture the imagination of our nation's teenage girls. When Allen removes her spike-heels a few tunes in because it was a "f**king stupid idea to try and perform in them", she’s greeted by a rapturous roar from the Topshop - or should that be New Look? - disciples that dominate the crowd.

Backed by a sprightly seven-piece band – including a bouncy brass trio whose moves would have Arlene Phillips panting with delight – Allen is on majestic form tonight. She shows off her rapid-fire rap skills on her 50 Cent parody ‘Nan, You’re A Window Shopper’, proffers some beautifully crystalline vocals on a heartbreaking version of ‘Littlest Things’, and turns the venue’s 16th century courtyard into a Kingston Town dance hall on her Mark Ronson-helmed cover of the Kaiser Chiefs’ ‘Oh My God’. Her songwriting skills aren't too shabby, either: ‘Friday Night’, with its euphoric chorus, bashment beat and tales of sozzled squabbling, manages to invent a musical sub-genre all of its own – shall we call it skargey-bargey? Only ‘U Killed It’, a rockier tune whose swirling chorus recalls Natalie Imbruglia’s ‘Big Mistake’, threatens to interrupt the carnival atmosphere.

Just over a year since she became a household name, Allen is showing signs of wanting to mature. She makes her influences explicit by inviting former Specials guitarist Lynval Golding onstage for a couple of knees-ups and takes a pop at George W. Bush by dedicating the sardonic ‘Everything's Just Wonderful’ to his term as US President. What’s more, a stripped-back, skankin’ cover of Blondie’s ‘Heart Of Glass’ sees Allen paying tribute to a feisty female who came before her.

Judging from her stage patter, Allen can be childish, puerile and, in dedicating ‘Friend of Mine’ to the school bully who later became a “crack-head b**ch”, a tad spiteful. But, when she admits that there are “so many things about myself that I despise” on the self-lacerating ‘Cheryl Tweedy’, you just want to take her round to your Nan’s for a steaming mug of tea and a nice chinwag. So do most of London’s 15-year-old girls, on tonight’s evidence. The upshot of this? The most compelling pop star of our times is in no danger of losing her grip.