Songs are rarely as “side one, track one” as the Rolling Stones’s new single Angry, which kicks off Hackney Diamonds, the band’s long-awaited full-album return to the Jagger-Richards songwriting partnership after 18 years. The Stones were hardly ones for creeping quietly around the door – Sympathy for the Devil, Paint It Black, Gimme Shelter and Brown Sugar have all teed albums off in the past – but Angry kicks it off the hinges with an opening riff that is instantly, inimitably theirs. In key and mood, it somewhat recalls another album opener: Start Me Up, which opened Tattoo You. But despite the band’s advanced age today, that 1981 song now sounds rather leisurely in comparison with Angry’s tight, energised strut. Jagger is massively entertaining throughout, dramatising a lover’s squabble with exasperation and bafflement: a really humanising performance that reminds us that for all their millions, rock stars can never be insulated from the ire of a pissed-off partner. “Don’t get angry with me / I never caused you no pain,” he begins, audibly on the back foot already – and then quickly complains that he, at 80, hasn’t had sex in a month. Perhaps not so relatable after all. Anyway, that doesn’t go down well, and relations deteriorate at pace. By the bridge he’s pleading “please just forget about me,” and he’s now trying to do something we’ve all done: end a relationship well, with dignity and harmony, but ending up mired in petty recrimination. He even attempts the classic gambit of suggesting one last shag for old time’s sake: “If we go separate ways … let’s go out in a blaze.” That doesn’t work either. “I’m still taking the pills / and I’m off to Brazil” he flounces, as the song plays out in a long, anthemic gospel coda. In time honoured fashion, Jagger goes spelunking for extra vowels so that “Brazil” ends up pronounced “Bra-zee-ow”. The whole thing is a complete hoot. The Stones’s genius has always been take the haunted, spectral melodies of American blues and flick the casino lights on to them, and so it is here. Done a cappella by a different singer, Jagger lines here like “I never caused you no pain” could have a purely harrowed quality – but he and the band cleverly wax and wane from minor to major chords, carrying this tale of alternating desperation and resignation. Producer Andrew Watt rightly allows for all manner of murk lower down the mix: growling, distorted bass from Richards and doom-portending piano by sessioner Matt Clifford. Between verses Richards and Wood double up on the riff, then swap back and forth some brilliantly groaning, lurching extemporised mini-solos: playing that suggests fun, freedom and creative hunger. This is also the first recorded performance of new drummer Steve Jordan, and some Stones aficionados might find his martial exactitude lacking compared with the almost invisible, mystical swing of the late Charlie Watts’s performances. But it’s sympathetic and impactful timekeeping from Jordan (given a nice touch of echo by Watt), that keeps the song marching along like a someone having a head-clearing mid-argument stomp round the block. Watts’s death reminded us of the mortality of the Stones, once so impossible-seeming, and it has surely preyed on their minds that they won’t have that many chances to write new albums. The quality here suggests they’re really seizing the opportunity – but on Angry, and at their boyishly buoyant accompanying press conference, they don’t sound at all freighted with nerves or fear. Instead, it situates them in a class of their own: rock-togenarians strutting back out to the world’s stadiums. Hackney Diamonds is released by Polydor on 20 October