John Mayer, Hammersmith Apollo, London

John Mayer has a lot of things going for him: talent, looks, wealth, fame. A roster of beautiful ex-girlfriends. But come on, give the guy a break; the rock-star life isn't always a bed of roses. The American tabloids have a hard time leaving Mayer alone and as he discovered last week, when he made a couple of unfortunate jokes about sex and drugs during an acoustic gig at London's Hard Rock Cafe, the British press are no more forgiving.

Over here, Mayer is mostly famous for the beautiful ex-girlfriends and the sex jokes. "All of which overshadows," he complains, to an adoring Hammersmith Apollo, "the fact that I actually play guitar." Furthermore, even when his considerable musical talents become apparent, Mayer must contend with a sceptical wider audience. Unlike his home country, the UK has a crippling intolerance for what some might call classic rock. It frequently feels as if anyone under 50 who enjoys a bluesy guitar solo is considered desperately uncool.

The band of seasoned professionals Mayer has assembled, however, look like a mark of credibility – as does the fact that his new album, Battle Studies, mimics the traditional rock tropes of Tom Petty, Fleetwood Mac, Neil Young and the like. The lynchpin of Mayer's band, his musical soulmate and the album's co-producer, is the drummer Steve Jordan, who has played with Eric Clapton and Keith Richards.

The show opens, as does the new record, with "Heartbreak Warfare", a driving and accusatory elegy for a difficult relationship. If Mayer wants everyone to forget about those exes, writing a break-up album may not have been the best idea. Next comes a brilliant cover of a blues standard, "Crossroads", which was made famous by Cream.

Mayer weaves musical history through the set at every opportunity, dropping Bob Marley into the heartfelt waltz "Gravity" and the Jackson Five into the ballad "Why Georgia", the latter taken from his 2001 debut, Room for Squares. An acoustic cover of Petty's "Free Fallin'" has become an integral addition to his set.

Some of his own songs have entered the canon – or so the ecstatic crowd response they prompt would suggest – including the poppy "Bigger Than My Body" and two mildly politically-minded tracks: "Waiting on the World to Change" and the thoughtful, brilliant "Belief", both from the 2006 album Continuum.

There is no doubt that Mayer has a faithful British following, big enough to both sell out the Apollo in a couple of hours and allow him to announce a Wembley Arena show in May. The lead single from Battle Studies, "Who Says", has a lyric ("It's been a long night in New York City/It's been a long night in ...") that is perfect for inserting the name of the relevant city, so whipping the crowd into a happy frenzy of recognition. Most of the time, Mayer has an easy charm – his stage banter runs the gamut from those inadvisable sex jokes to earnest and geeky philosophical musings.

Though the first half of the set is magnificent, the frequent solos – drum solos, guitar solos, keyboard solos, guitar solos, yet more guitar solos – wear thin after a while. There are, for example, a few yelled requests from the crowd for favourites from the new record that are ignored in favour of a series of four-minute instrumental noodles. But for an artist who might be thought of as safe, Mayer rewards his fans by taking an awfully healthy number of liberties with his songs on stage – and one improvised slow jam too many seems a small price to pay for that.