The Last Shadow Puppets, Hammersmith Apollo, London

Monkeys overshadow the Puppets' show

In the seven months since their first gig, the acclaim and attention The Last Shadow Puppets have received has been incredible. There has been a No 1 album, breakthrough-artist awards, Mercury Prize nominations and celebrity girlfriends along the way, feats that seem even more remarkable when you consider that the band make such a gloriously unfashionable racket.

But this sensational rise to rock'n'roll eminence is not what it first appears. You see, The Last Shadow Puppets have a trump card up their sleeve that has gifted them a few shortcuts along the road to victory. There have been no half-empty pub gigs on a rainy Tuesday night in Bethnal Green, no traipsing around the country in a clapped-out Transit van, and, perhaps most importantly, no need to break their back for commercial success.

The trump card, of course, is Alex Turner, a man whose day job as an Arctic Monkey means that he comes complete with an adoring fanbase, critical acclaim and radio airplay guaranteed. So far-reaching is his appeal that he could doubtless record an album of Mongolian folk chants and it would still top the charts.

And tonight, despite all the pomp, praise and adulation this side project has received, it's clear that Turner is still the star – the man the leering, bleary-eyed crowd are here to deify. They may have the album, they may well know the songs, but the sight of the London Metropolitan Orchestra setting up at the back of the stage still causes bewilderment among the riotous beer boys at the front of the stage.

Perhaps they're confused as to why Alex Turner and Miles Kane bother to go to such considerable effort and expense to bring an orchestra along at all. It's to their credit that they do, though, and it's proof, if proof were needed, of a fervent belief in the quality of their songs. However, it's also a clear indicator of how privileged the two men are in comparison with their peers.

As the lush string arrangements fill the air and Turner and his doe-eyed sidekick take the stage, the mood is decadent, melodramatic, and has a sense of impending catastrophe. Their monochrome suits may be slightly ill-fitting, but it's of little real significance since the music has been particularly well tailored. This is choreographed indie for adults: sophisticated, brooding and intelligent.

The ice-cool dual crooning effortlessly drowns out the terrace chants of "Ooh-Ah-Alex-Turn-Aaaahh!" and, as a sinister-sounding guitar wails, the band burst into their debut single, "The Age of the Understatement". Live, the song sounds exactly as it does on record, which for plenty of bands would be a problem, but such is the fat-free precision of the sound that a duff note or out-of-tune guitar threatens to disrupt the refinement. The drums gallop, strings drench the air and guitars weave in between the rhythms effortlessly, producing a controlled explosion of sound and theatre that sounds part Scott Walker, part Shirley Bassey.

Between songs, Turner and Kane are exceedingly polite, reeling off the cabaret one-liners. At one point, Turner addresses the balcony, and you're almost certain he's about to ask them to rattle their jewellery, John Lennon-style. Instead, he dedicates the song to his grandmother. The middle-class pandering on display seems almost of another period: the era of The Ed Sullivan Show, the twist, swooning girls and rock'n'roll bands aiming to be respectable lads. It's as if the Sex Pistols never happened.

However, the façade wears thin relatively quickly and we're just left with the songs. It's a shame but, despite their undeniable charm, Turner and Kane's side project is actually something of a one-trick-pony, with each song far too similar to the last. Their sound may be unique among their peers and the critical acclaim genuine, but if the band are ever to step outside the Arctic Monkeys' shadow, they'll need to rein in the pastiche and throw a few more big ideas into the mix.