Those Kanye West fans here to check out his latest protege might be surprised at how quickly he has come on. Just five months after being discovered, he is playing arena shows with a set of 40 songs – at least 27 of which are among the best ever written – and the nation loves him.

For the regulars, however, a Paul McCartney show runs through reassuring rituals. There is wonky dad-wiggling and Hofner basses are held worshipfully aloft. There are the stories about watching Hendrix play Sgt Pepper’s live just two days after its release and of how McCartney wrote Blackbird in support of the civil rights movement. He pays tribute to the Beatles he has lost with Here Today, his imagined conversation with John Lennon, and with George Harrison’s Something, opened on solo ukulele before it gloriously expands. The entire flame-and-firework budget is blown on 30 seconds of Live and Let Die, and the crowd waves signs reading “NA” during Hey Jude. The Macca spectacular is one of finely honed brilliance.

It’s also a reminder of why McCartney’s genre-straddling canon is second to none. There is Helter Skelter, which invented heavy metal, and his first live performance of Temporary Secretary, the cranky electronic ditty that offered an early taste of techno. Keeping songs from 2013’s return-to-form New to a minimum, McCartney tosses out culture-defining classics – Eight Days a Week, We Can Work It Out, Paperback Writer – in the way that most bands throw in album tracks. He makes the O2 feel special with a UK premiere of Another Girl, from 1965, and by granting one sign-waver’s wish for Sir Paul to autograph his wife. He even brings out a protege of his own, up-and-coming rhythm guitarist Dave Grohl, who riffs his heart out in I Saw Her Standing There. Good spot Kanye: this guy’s got promise.