Jessie J, Scala, LondonRichard Thompson, Royal Festival Hall, London

The industry insiders' current favourite seems to have come from nowhere, and it's difficult to see what else is there besides her kooky image

It's been a short hop, skip and jump between Brit School and Brit Awards for Redbridge-born Jessica Ellen Cornish.

After releasing just one single ("Do It Like a Dude", a song which has shifted more strap-ons than Ann Summers), she has won both the BBC Sound of 2011 poll and the Critics' Choice awards at the forthcoming Brits, like a heavyweight boxer unifying the world title belts.

Granted, this kind of consensus is an increasingly common occurrence given the cowardice of music hacks and industry insiders who just want to be seen to back the winning horse (rather than vote with their hearts), but there's nonetheless something a little eyebrow-raising about the rise of Jessie J.

Especially as she'll insist she's "real" and "normal" with one breath, and in the next tell us that she offered such-and-such a song to Alicia Keys, and that she found herself staring into a toilet mirror in Los Angeles two years ago and decided she had to leave the music industry. She's only 22 now (officially, in any case, though that might be a Florence Welch "22"). How many "real", "normal" kids even make it to Los Angeles by the age of 20, never mind find themselves in a position to opt out of the biz?

We know so much, these days, and yet so little. Perhaps the only thing to do is sigh with resignation and accept that whatever clandestine machinations bring people like Jessie J to the fore, that's just how pop stars are made now, the only remaining question being: is she a good one?

She's got the image. With her sleek black hair, high cheekbones and scarlet lips, she looks so much like Siobhan Fahey in her Shakespear's Sister days it's freaky, although whoever put that emerald-green corset together with those cowgirl leggings needs to go back to stylist school. She's got a reasonably strong showbiz-soul voice (if a little on the shrill side), like a no-frills Aguilera, and livens it up with bits of street-chat rapping and muck-around sex noises. And she's fairly funny between songs, talking in identical cadences like Catherine Tate's Lauren. I keep expecting her to ask: "Is the Lord your shepherd, Miss?"

But the songs? On first hearing, from the strutting rock-funk "Mama Knows Best" to the insipid reggae-lite of "Stand Up", they're so middle of the road it's baffling. She tells us to shush for "Big White Room", apparently the first song she ever wrote, which she's recording live tonight for her album, warts and all in one take. Her guitarist bites his lip and shakes his head slowly, like guitarists do, and Jessie makes it through with no bum notes. She does a little victory jig, and announces: "History in front of your eyes!"

For the next single, a piece of summery swing called "Price Tag", the singer is joined for a rap by fellow up-and-comer Devlin. It's all perfectly inoffensive stuff, but I can't work out what Jessie J is for. A ruder (in both senses) Betty Boo? A British Gaga without the strangeness? Indeed, she hints at the latter by referring to her fans as her "heartbeats", then explaining, "I was gonna call you something like 'monsters', but..."

The jury may be having a tea break, but Jessie pre-empts any verdict of foul play or conspiracy by proclaiming: "I'm just trying to bring some love into the world. I don't have no ... Illuminati stuff."

Wearing a black beret and holding a powder-blue Stratocaster at Bren gun height, Richard Thompson peers quizzically through a light fog, looking for a moment like Pike from Dad's Army on sentry duty, then he's away into "The Money Shuffle", an anti-banker polemic which rhymes "Sound of thunder" with "Lehmans going under".

A skittish, stuttering presence, the folk-blues veteran is quick with a self-deprecating sarcastic quip, mocking the material on his Grammy-nominated Dream Attic album, which comprises the first half of the show, as being "depressing". Which, on songs such as "Sidney Wells" (the tale of a serial-killing trucker) and the self-explanatory "Crime Scene", it indubitably is, but, this is nothing new. The 61-year-old has always been fond of a murder ballad, right back to "Crazy Man Michael" from his Fairport Convention days. You could almost call him a more genteel Nick Cave when he's in this mode. The Quite Nice Seeds, perhaps, or Coffee-Grinderman.

He's more widely seen, however, as a redeemable Mark Knopfler, or the Eric Clapton you don't feel you have to hate.

Very much the guitarist's guitarist, he's all too fond of showing off his unquestionable dexterity by doubling, even trebling, the length of his songs with epic noodling outros in which his band of dependable greyhairs also play their part, with bassist Taras Prodaniuk bending over backwards in technical ecstasy and Pete Zorn chipping in with an assembly of saxes and flutes.

As his "hits" section reaches its finale with an audience-participation "Tear Stained Letter", I do, at least, get what Richard Thompson is for. But – when the soloing is into its seventh minute – maybe he's not for me.

Next Week:

Simon Price asks: is there life on Bruno Mars?

Rock and pop choice

Bryan Ferry holder (with Neil Tennant) of the World's Least-Stereotypical Geordie title, relaunches Roxy Music at the Metro Radio Arena, Newcastle (Wed); then visits the Clyde Auditorium, Glasgow (Thur & Fri); and further venues. Nick Heyward reforms his Eighties jangle-poppers Haircut 100 for a one-off gig at London's Indigo2 (Fri).