Billy Joel is 74 and not shy about it. “Don’t get your knickers in a twist,” he cautions as he steps out from behind his grand piano for the first time, “I ain’t no Mick Jagger”. He struts comically through a burst of Start Me Up to prove the point.

Later, he watches himself on the screen and gasps: “Oh Christ, it’s my old man. Hello Dad.”

Joel looks like a mob boss who came up the hard way and talks like a standup comedian riffing on the career of Billy Joel. He wasn’t always this relaxed. Back when he was the most unhip of megastars, he couldn’t pretend that the critical sneers weren’t bugging him.

Thirty years ago, he quit releasing new songs all together. Now, though, nobody cares what Rolling Stone considered cool in 1982. Since 2014, his triumphant Madison Square Garden residency has turned the writer of New York State of Mind into the musical equivalent of the Empire State Building.

The residency has produced a precision-tooled entertainment machine, from covering A Hard Day’s Night to bringing on Joe Jonas for Uptown Girl. “The bad news is we don’t have anything new to play,” Joel says slyly. “The good news is you don’t have to hear anything new.”

As a songwriter, he has two lanes. He’s the Piano Man, singing theatrical ballads about down-on-their-luck New Yorkers, and he’s an expert pasticheur, re-inhabiting the sounds of his youth: Motown, doo-wop, Tin Pan Alley. Sometimes this wiseguy is a wise guy.

Fan favourite Vienna is a beautiful warning against being maddened by youthful ambition, while We Didn’t Start the Fire’s apocalyptic ticker tape, mocked and parodied though it is, was written to remind fretful young people that the world has always been a mess.

Songs like Big Shot recall Joel’s former chippiness but his final act has a warm glow of contentment and generosity. On this golden evening in Hyde Park, the cameras often dwell on the audience, who take the last chorus of Piano Man for him. “It’s me they’ve been coming to see,” he sings. “To forget about life for a while.”