ock'n'roll is notorious for its tales of bad behaviour: throwing TVs out of the window, mountains of cocaine, parades of groupies … but you won't find any of that here. Peter Asher, brother of Jane, one half of Peter and Gordon, and super-successful producer of acts such as James Taylor and Linda Ronstadt, appears to be about as nerdish and clean-living as a 60s/70s music industry veteran could be. Although that might just be what he wants us to think; what are the chances Asher is a complete reprobate away from the camera, and is just brilliant at hiding it? That glasses and ruffled shirt front combo definitely reminds you of someone a tad more sleazy, even before Asher himself reminds you about it in the final credits.

Whatever the truth, Asher by any standards carved an amazing path, making the absolute most of being in the right place at the right time. Smartly structured around Asher's anecdotes-and-music live show, the film stitches together a collection of clips, audio and musical performances that gallops through his personal backstory. His luckiest break, of course, was that his early partnership with schoolfriend Gordon Waller (modelled, it turned out, on the Everly Brothers) benefited from cast-off songs handed over by his sister's boyfriend, one Paul McCartney; there's an amusing moment where we hear John Lennon's sneer at the lyric of what would become Peter and Gordon's first and biggest hit, A World Without Love: "Please lock me away …" "Yes". While the film clearly acknowledges the debt to McCartney's songwriting (which presumably Lennon vetoed for the Beatles), it's perhaps not quite ready to admit that without this connection, none of what followed would have happened at all.

At one point Asher says he wasn't much of a pop star, and subsequent events suggest he was probably right. He appears to have been more comfortable away from the spotlight, thereby allowing him to become a ubiquitous figure in the Beatles' orbit in swinging 60s London to which the title alludes. He was a co-owner of supercool art gallery Indica (where Lennon first met Yoko Ono), though given it only lasted two years, possibly he wasn't all that great at that, either. It was the Beatles' connection, though, that allowed him to really come into his own, when he was appointed head of A&R at the newly formed Apple Records, with his own top floor office in the Savile Row building.

Asher's big discovery was Taylor, who had relocated to London after failing to get anywhere at home in the US; after producing Taylor's debut album (which with characteristic modesty he says he messed up with Beatles-style orchestration), Asher followed Taylor to Los Angeles and settled into a quietly impressive second act as a producer and manager. After producing Taylor's breakthrough second album, Sweet Baby James, Asher became a key figure in 1970s Californian soft rock, overseeing acts including Andrew Gold, Kate Taylor, JD Souther and – most successful of all – Ronstadt. Admittedly, this now looks a tad middle of the road, a musical era since vanquished by punk and new wave, but Asher later got on board with credibility-stoking artists such as Cher, Diana Ross and 10,000 Maniacs, and even produced albums by Boyzone and Morrissey.

Throughout this parade of achievement, Asher cuts an impressively self-possessed figure, unassuming in many ways but also not hiding his light under a bushel. The appreciation he gets from his big-name collaborators is clear enough, but he also gives houseroom to somewhat more tangential figures, with Carole King in particular coming across strongly. But it's the interactions with late former partner Waller that are probably the most resonant, with the virtual duet Asher sets up being especially moving.