For reasons that should be clear from my bio picture, I have a soft spot for Carole King, because of her hair. On the cover of Tapestry, it’s a giant, wispily centre-parted, glorious statement, effortlessly upstaging the cat in the foreground of the picture. And Beautiful does a good job of persuading you that, by the 1970s, Carole deserved her massive poodly hair, bless her. It’s not like the show’s writer, Douglas McGrath, has set himself a particularly difficult task, but it’s still worth praising a lovely central performance from Katie Brayben, who plays King with a gentle subtlety that helps centre the showbiz lights on a real person.

The hair begins in a bouncy pony-tail as 16-year-old Carole persuades her mother (tart, dryly funny Glynis Barber) to let her go to Broadway and pitch her song to music producer Donnie Kirshner (Gary Trainor). The song is ‘It Might As Well Rain Until September’, which almost reaches the Top 100. She starts a romantic and professional partnership with cool college kid Gerry Goffin (Alan Morrissey), and the hits come fast and climb higher. These early 1960s songs – ‘Some Kind of Wonderful’, ‘Take Good Care of My Baby’, ‘Will You Love Me Tomorrow’ – were designed to have a mass-market appeal, to get picked up by a group with a ready fanbase, to say ‘boy meets and/or loses girl’ in three minutes. It doesn’t make much sense to try and pretend that they have any particular relevance to Carole and Gerry’s own story. Instead, Beautiful uses them as an excuse to bring on The Drifters and The Shirelles, in snappy suits and beehives, to sing them in hilariously tightly choreographed set-pieces. These ensemble moments are some of the most enjoyable scenes in the show.

Providing an excuse for more of them, Cynthia Weil and Barry Mann (Lorna Want and Ian McIntosh) join Kirshner’s industrious team of songwriters and enter into friendly competition with Goffin and King, writing ‘On Broadway’, ‘We Gotta Get Out of This Place’ and ‘You’ve Lost That Lovin’ Feeling’. Want and McIntosh both give excellent supporting performances, and their energetic chemistry provides a relief from and counterpoint to the strains that start to appear in Carole and Gerry’s relationship. Having married very young when she became pregnant, by the mid-60s they have two girls, and Carole’s hair is suffering in a practical but unattractive updo.

The second half begins on a darker note, as Gerry has a nervous breakdown and a series of affairs. Morrissey’s twitchy, hopeless confusion in these scenes gave me a brief panic that he’d forgotten his lines a couple of times, but when Carole finally leaves Gerry, Beautiful propels itself towards the highpoint of her career, in the multi-Grammy-award-winning album, Tapestry. The songs on the album are presented in the show as the anthems of a shy, quiet woman finally claiming her own emotions and talent, and Brayben does great songs like ‘It’s Too Late’ and ‘So Far Away’ full justice. Her hair swings curly, long, and free.

Beautiful does what a good West End or Broadway musical is supposed to do: it crams in the tunes. Its plot is mostly narrative-by-numbers, and McGrath has obviously trimmed and tailored King’s life so that the story can end triumphantly onstage at Carnegie Hall. But there are some witty lines (Cynthia on ‘Who Put the Bomp’: “Well … it’s certainly inquisitive.”), despite the need for each scene to provide swift exposition between songs, and the scales are sensibly tipped towards light-heartedness throughout. It’s not one of the great musicals, and it doesn’t really seem to have ambitions to be – its mild commentary on race and ethnicity in mid-twentieth-century America ain’t West Side Story – but I left smiling, and let my hair down.

Beautiful is playing Aldwych Theatre until 13 February 2016. For more information and tickets, see the Aldwych Theatre website.