It was billed as a “historic event” in which two of rock’s towering icons performed a co-headlining show for the first time in Britain, heralded with a short video compilation of vintage clips of Bob Dylan and Neil Young performing live over the years, tracing their twin careers through decades of unpredictable shifts and changes.

Should the organisers of Hyde Park’s one-day festivals British Summer Time have assumed said unpredictability was now a thing of a past – Dylan and Young are now 78 and 73 respectively, ages at which one might reasonably expect even the hottest-burning firebrand to have settled down a bit – they were in for a rude awakening.

The gig had barely been announced before Young issued a statement via his website, decrying the show as “a massive fuck-up” and declining to take part at all unless somebody did something about its sponsor, Barclays, “a fossil-fuel funding entity”. Evidently rattled – the promoters were presumably expecting something more along the lines of how much he was looking forward to seeing his fans and rockin’ London – Barclays’ name and the British Summer Time branding was discreetly dropped, the gig went ahead, but notice had been served: age has not rendered two of the most unbiddable figures in rock history any more biddable.

Facebook Twitter Pinterest Neil Young was in a crowd-pleasing mood in Hyde Park on Friday. Photograph: Matthew Baker/Getty Images

The usual sense of trepidation attended Neil Young’s performance – he’s still entirely capable of making such an unyielding racket onstage that people feel impelled to write letters of complaint to the national press, as happened in Ireland during his 2012 tour with Crazy Horse – but he seems in uncharacteristically crowd-pleasing mood. His set is largely drawn from 1990’s Ragged Glory, the album that cemented his reputation as the godfather of grunge, and his biggest seller, 1972’s Harvest: its controversial track Alabama making a reappearance, presumably as a result of the state’s recent abortion ban. He rolls out the hits – Heart of Gold, Like a Hurricane – and curtails his penchant for onstage jamming to accommodate an hour and a half set time.

Songs that have been known to last weeks in their live versions – Love and Only Love, Words – zip by: only a concluding Rockin’ in the Free World is extended, with a succession of false endings. He leaves the stage smiling.

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Enter Bob Dylan, eager as ever to demonstrate that when it comes to unbiddable live performances, the boss is in town. It’s an article of faith among his devotees that his gigs represent astonishing nightly feats of musical reinvention, in which a consummate artist presents his oeuvre not as a back catalogue carved in stone but a kind of living entity, constantly shifting and changing according to his mood, and that anyone who disagrees belongs in the dunces’ corner alongside the guy who shouted “Judas!” at him in 1966: entire books have been written on the subject, in which the changing emphases placed on certain words during different performances of All Along the Watchtower are discussed in depth and his between-song utterances – if he’s in a particularly garrulous mood you might get a “Hello” – are compiled and pored over for deeper meanings.

For the less committed, watching him live is as baffling and frustrating experience as money can buy, in which his voice – now a ruined phlegmy gurgle – and apparently unquenchable desire to redecorate his material with completely different melodies to the ones he originally wrote mean that every new number brings with it a heated debate as to which song he’s actually performing, the debates occasionally going on longer than the song itself. Tonight, both factions seem well represented: the true believers are going nuts at everything he does; equally there’s a steady stream of people leaving long before he quits the stage.

At risk of sounding equivocal, you can see both sides of the argument: there are moments when songs spark into new life – not least Like a Rolling Stone, its old sneering anger replaced by a world-weary melancholy, its tune intact enough to provoke an audience singalong – and moments when you have literally no clue what’s going on up there and wonder if anyone does outside of Dylan and his band, the latter clearly drilled to perfection on their boss’s foibles: “Oh my God, this is Make You Feel My Love” cries out a voice in the crowd midway through his most famous latterday composition, a tender ballad of love that he’s somehow succeeded in transforming into something weirdly menacing.

For his part, Dylan appears to be having an absolute whale of time: he unexpectedly keeps grinning at the audience and at one point quits the piano to strike a series of vaguely Elvis-ish poses at the microphone. But then, why wouldn’t he? A sizeable proportion of the audience adores him, another chunk evidently has no idea what he thinks he’s playing at, which, for Dylan, amounts to unbiddable business as usual.