The rock legend in the autumn of their years who chooses to release a new album is well advised to get themselves an angle. If the music that made you legendary was written and recorded long ago – and is highly unlikely to be displaced in the public’s affections by anything you do now – it’s good to have something that suggests a sense of purpose, beyond just adding to an already vast back catalogue for the sake of it.

We’ve recently seen it with Bob Dylan’s Rough and Rowdy Ways, rooted in its jawdropping 17-minute survey of American political history, Murder Most Foul; and with Bruce Springsteen’s Only the Strong Survive, with its canny covers of soul and R&B classics. And an angle is clearly something that has occurred to Paul McCartney, too. From its title referencing a road in the suburb of Liverpool where McCartney spent his early childhood, to the circumstances of its launch – the first single Days We Left Behind was premiered not on YouTube or Spotify but BBC Radio Merseyside – his 27th studio album has been presented as a nostalgic look back at what you might call his pre-Fab years.

The idea has certainly generated excitement and not a little emotion on the part of fans. McCartney seems to have spent the last few years crossing the Ts and dotting the Is on various aspects of his past: reworking the footage of the Let It Be recording sessions to cast it in a more positive light than the 1970 film of the same name; completing the one song left unfinished during the mid-90s reunion of the surviving Beatles; releasing a documentary designed to remind the public that, for all the critical opprobrium thrown their way, Wings were absolutely huge in the 1970s. A burst of sentimental autobiographical reminiscence adds to the faint but detectable sense that his career is drawing to a close.

But before we get too maudlin, it’s worth noting that The Boys from Dungeon Lane is not, by any stretch of the imagination, a concept album. There are certainly songs here that fit the advance billing, of which more later. But there’s also Mountain Top, a song about a girl tripping on mushrooms at Glastonbury, set to a kind of 21st-century update of the oft-maligned subgenre record collectors call toytown psychedelia. “Pumpkin pies in the skies also try to hypnotise,” sings Macca over a harpsichord backing, his vocal put through an effect that approximates the tremolo sound of a Leslie speaker – a technique pioneered on Tomorrow Never Knows – while producer Andrew Watt gets to go nuts with the phasing effects and the I Am the Walrus-evoking bursts of looped spoken word. There is Momma Gets By, which revisits the theme of Lady Madonna in noticeably less upbeat mode, big on sighing strings; and Life Can Be Hard, an unashamed and particularly sparkly example of what John Lennon once waspishly dubbed “Paul’s granny music” – the Tin Pan Alley-indebted aspect of his songwriting that gave the world When I’m Sixty-Four and Your Mother Should Know – with a hint of Dixieland jazz in its arrangement.

There are Ripples in a Pond, Come Inside and We Two, the kind of lyrically slender love songs for which McCartney would have been critically clobbered in the 70s, but which these days seem impossibly charming, not least because they demonstrate his extraordinary melodic skill: listening to We Two, you find yourself boggling a little at the sheer volume of deftly executed twists and turns he manages to cram into a something so ostensibly slight.

You could argue the songs that arrive as advertised are nothing new, thematically speaking. The Beatles were harking back to their childhoods 60 years ago, their memories jogged by LSD: “It was a case of four Scousers exploring inner space and just finding more and more Scouser down there,” as their press officer Derek Taylor wryly remarked, hence Penny Lane and Strawberry Fields Forever, which some Beatle historians insist were intended as part of an album devoted to their Liverpool youth. In McCartney’s 21st-century oeuvre, Queenie Eye, Early Days, On My Way to Work, That Was Me and indeed most of 2012’s Kisses on the Bottom – comprised largely of songs he remembered his father playing “when I was a kid and had family sing-songs” – have boasted a distinctly sepia tone.

That said, there’s no doubt that the similarly rooted songs on The Boys of Dungeon Lane pack a considerable emotional punch. If McCartney’s latter-day voice – noticeably thinner and shakier than it once was – is a problem when essaying Band on the Run on Saturday Night Live, it’s curiously effective here, a constant reminder that these are songs written by an octogenarian, that the events they’re describing happened a very long time ago.

As You Lie There recalls an unrequited crush to an accompaniment that, with its episodic structure and guitars fat with compression and distortion, seems haunted by the ghost of Wings, while Salesman Saint details his parents’ financial travails, sliding into a burst of 40s swing at its close. Down South recalls hitchhiking in the company of George Harrison: there’s something oddly moving about its understated conclusion: “It was a good way to get to know you.” The duet with Ringo Starr, Home to Us, barrels along in a manner that vaguely recalls Oasis’s She’s Electric – how’s that for circularity? – powered by the infectious sense that everyone involved is having a high old time.

As is usual with contemporary McCartney, there are a couple of songs that don’t quite click – the rocking Come Inside, the unremarkable First Star of the Night – but The Boys of Dungeon Lane seems noticeably more purposeful than a lot of his 21st-century output: if the advance publicity seems more like an angle than reflection of its thematic unity, it still feels focused in a way that 2013’s New or 2018’s Egypt Station did not. Perhaps his approach was driven by a sense of the clock ticking: if you’re going to make an album at 83, you’d better make something that counts, which The Boys of Dungeon Lane does.

• The Boys of Dungeon Lane is released 29 May