It's 10 minutes into the show, and Jessie J is already playing air guitar. Playing it? She's wringing the life out of it – squeezing the neck and slashing at the strings, as she blares the empowering platitudes of a song called Sexy Lady. "Give it everything you got," it runs. "Show 'em you're a sexy lady, work it till it's burning hot."

Who, in 2013, could maintain a straight face while singing a power-rocker titled Sexy Lady? Jessie could. The song, and air guitar, are the Essex-born singer in a nutshell: naff, good-hearted and prone to motivational guff that seems incongruous coming from a Brit – even one with an emergent transatlantic flatness to her vowels. Little wonder she invited mockery by the Twitterload as a judge on The Voice, which she recently left after two seasons.

"It's not very often that I pay attention to the haters," she assures us tonight. Well, she would say that: her biggest hits – Who You Are, Domino – are homilies about being yourself and ignoring the bullies who might take issue with your peroxided pixie-cut and white Lycra bodysuit. Yet there's a big-sisterly kindness that suggests her teenage following could have a far worse role model. And the fans, who are overwhelmingly female, repay her by already knowing almost every song from the new album, Alive; those they don't, they bounce along to anyway.

If half of Jessie consists of Americanised earnestness, the other half is pure melismatic lungpower. The blast-force delivery drowns out Dizzee Rascal, who pops in to bark a verse of the recent single Wild, while another guest, the American R&B star Brandy, just about holds her own on Conquer the World. The oversinging is Jessie J's Achilles heel; it matters less when the song is a piece of glorious fluff, as in the opening Price Tag, but power ballads such as Who You Are send her into an octave-scaling frenzy.

Yet things haven't always been this way. A strobe-lit "club" segment, with back projections of bass speakers, is a reminder that before she won the BBC Sound of 2011 poll, she was almost one of the cool kids. This part of the set throws up unexpectedly cracking electro versions of Do it Like a Dude and LaserLight, rivalling Katy B for pop hipness. But then, can Katy wear a pixie-cut like Jessie?

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