R.E.M. Royal Albert Hall, London

Michael Stipe falls to his knees. Quick as a flash, some wag in stall G shouts, "While you're down there, Michael!"

This one-off R.E.M. gig, a fundraiser for the ICA and a public launch for Accelerate, their 14th album, arrives against the backdrop of the news that the band's lead singer has come out. Again.

This time around, the "news" broke in an interview with US magazine Spin, the New Zealand Herald picked it up and ran with it, and it rippled around an unsurprised world. After all, it feels as though Michael Stipe has come out more times than a flasher's knackers.

He first described himself as "a queer artist" in Time magazine in 2001, but there had been rumours for years, right back to the day in December 1992 when Nicky Wire saying "In this season of goodwill, here's hoping Michael Stipe goes the same way as Freddie Mercury" on stage caused such a pious furore (a remark that was misinterpreted, by the way).

It's been a long process. Maybe he'd been trying to tell us all along. ("Consider this/The hint of the century/Consider this/The slip that brought me to my knees ...") A couple of years ago, in a joint Q interview with Stipe and Rufus Wainwright, the latter began a sentence: "Since we're both gay men ...", prompting the former to quip, "That's easy for you to say." Now we know for sure.

R.E.M. always possessed a certain mystique, a band with other, non-obvious agendas at play, whether sexual or intellectual. (Those mumbled, gnomic lyrics didn't harm that impression.) From the Deep South they crawled, an anomaly even then, among acts from the Whistle Test-endorsed wave of Paisley Underground and New Country, despite the traditionalist chime of Peter Buck's guitars.

Their slight but definite difference has been sufficient to sustain the attention of a loyal following for a quarter of a century (and indeed to justify an irritating sacred cow status among critics), but if tonight proves anything, it's that R.E.M. aren't in the mood for resting on their laurels.

The way they rage into the set opener "Living Well Is the Best Revenge" is a surprise. There isn't an ungrey hair on the stage (and in Stipe's case, no hair at all), but close your eyes and you wouldn't think it. Wearing what looks like a parole suit, this funny little shaven monkey-man – he looks like the penultimate picture in one of those "ascent of man" graphics – is an unquestionably charismatic leader, leaning into the void so that his mic stand and body form a letter X.

"It's such a great honour to be here at Wembley for the seventh night in a row," he jokes, before praising the acoustics of the Royal Albert Hall, and the smartness of support act Robyn Hitchcock in choosing to play an acoustic set to match. "But you're not gonna get that from us. It's gonna be ... loud."

Which it is, relatively speaking (in other words, it's R.E.M.-loud, not Slayer-loud), as they clatter through Accelerate. It's often their more haunting moments, though, that hit the spot. Sixteen years on, "Drive" still feels like a bitterly ironic, reproachful epitaph for the entirety of pop culture, paraphrasing David Essex of all people: "Hey kids, rock'n'roll/ Nobody tells you where to go, baby..."

They're in uncharacteristically playful mood. At the end of "The Great Beyond", Stipe hurls his lyric sheets into the crowd (and then issues the schoolmasterly instruction: "If you have more than one, please share with a neighbour"). Bassist Mike Mills joins the fun, going on a spotlit walkabout up the aisles.

There's no "Shiny Happy People". Which annoys me. You can't unleash an earworm on the world, then disown it like it had nothing to do with you. In the way of hits, there is "Losing My Religion", its mandolin melody one of the loveliest in pop's history, the mildly annoying "Imitation of Life" (yes, Michael, we get it, modern culture is artificial) and "Man on the Moon".

As I look around everyone singing lines like "I'm pushing an elephant up the stairs", it occurs to me that had my life panned out differently, it might have been Stipe and not, I dunno, Morrissey upon whose every word I hung. And you know what? That might not have been such a terrible outcome.