HOW do they do it? Exactly a year since they opened their latest world tour in Boston, the Rolling Stones arrived in their own backyard. The British leg of their A Bigger Bang world tour began last night at Twickenham, not two miles from where they began their extraordinary odyssey 43 years ago in the more modest environs of the Station Hotel in Richmond.

“You go round the world ten times and you end up back where you started,” Mick Jagger said as he led the band into Streets of Love, a song from the current album with an unusually confessional quality.

This latest chapter has been an unusually gruelling and accident-prone trek. They have played huge, groundbreaking events in Brazil, China and at the US Superbowl. But a tranche of dates had to be rescheduled after Keith Richards fell out of his tree and had to undergo brain surgery (Jagger introduced him as the band’s “chief headbanger"). Two more shows in Spain were postponed last week when Jagger succumbed to laryngitis. Charlie Watts has bounced back from throat cancer and a car accident. And Ron Wood (“The Renoir of rock”, as Jagger called him) has been on and off the wagon more times than a faulty wheel. But still they keep on coming.

A downpour before the show failed to dampen the crowd’s spirit as the band took to the stage amid fireworks and images of space debris. A vision of Guggenheim-inspired Art Deco, the huge stage structure was lined with members of the audience standing along “battlements” above and behind the performers. Jagger, an impossibly spindly and spiky figure in tight black trousers and spangletastic shirt, barked out the lyric of Jumping Jack Flash, while the Lazarus-like Richards hunched over his guitar and chopped out the riff with a woozy enthusiasm. Wood contributed a succession of unusually brisk and well-organised solos and Watts, with the band’s “invisible” bass player, Daryl Jones, maintained their reputation as the staunchest rhythm section in rock’n’roll.

The set included a handful of new numbers, including a swashbuckling Rough Justice, and one or two rarities such as Sway, during which Jagger, in particular, struggled to replicate the recorded performance. But the majority of the set was comprised of old favourites. A chunk of stage hydraulically detached itself and carried the group about 200 yards into the crowd as they played Miss You, a tremendous touch of theatre. They stayed in the middle of the sold-out stadium for Get Off of My Cloud and returned to the mothership, by this time overhung by a huge, lolling inflatable tongue, as they played Honky Tonk Women.

“If you start me up, I will never stop,” Jagger sang, and rarely has a truer word been voiced in song. The Stones may be long past their prime, and an anachronism to some. But watching them tear into the home stretch of Sympathy for the Devil, It’s Only Rock’n’Roll, Brown Sugar and Satisfaction was to see a group still magnificently, unrepentantly and quite joyously fit for purpose.