Hair, Gielgud Theatre, London

Critics always say that the most important element in a musical is the libretto, or book. Audiences don't care about this so much if the music is good, hence the popularity of Verdi, Puccini, and Lloyd Webber.

The great thing about this joyous production of the mother of all rock musicals, a total transplant of the recent Broadway revival, is that it makes a bad book look better and the already good music sound great.

The book in this case – by James Rado and the late Gerome Ragni – is a collection of protest clichés, love-in songs and hippie high fives among the Greenwich Village "tribe" where Claude (Gavin Creel) dreams he doesn't burn his draft card and goes to war in Vietnam.

In effect, he wakes up and does go to Nam and gets killed. Diane Paulus's production pulls the clever stunt of turning the protest into a lament for Claude as the tribe "let the sunshine in" and disperse through the stalls, leaving a corpse in uniform out in the snow. It's a stunning conclusion, managing to avoid both glutinous sentiment and mawkish piety.

At this point you realise the production has also managed to celebrate the innocence of youthful rebellion with its own built-in safety valve of satirical leg-pulling: Claude is ridiculed by his own parents who are token figures of ridicule anyway, until they accept that the hippies are a harmless bunch of nice guys with good tunes and bad hair and don't mind joining in themselves.

Hair was never really an underground, or even alternative, show: it was manufactured for commercial consumption from the off. And the score by Galt MacDermot, with a handful of chart-topping numbers and a bountiful mix of great jazz ballads, raw blues and choric anthems, remains as irresistible as ever: the "Hare Krishna" chorus elides into the "Where Do I Go?" Act I finale in which the cast's nudity is now delivered as a graceful and moving statement of helplessness and vulnerability.

There's been a considerable sharpening up of a lively vaudeville sequence in which war-mongering is book-ended with the assassination of Abraham Lincoln (played by a black woman in a top hat); to the accompaniment of a Jimi Hendrix-style guitar riff, Claude pushes a flower down the barrel of a rifle and is then born aloft in a Deer Hunter nightmare.

The only revival of Hair I've seen since the opening London version (which ran for years at the Shaftesbury Theatre), at the Old Vic 15 years ago, couldn't surmount the essential silliness of Claude and Berger and the rest.

This production does, partly due to the very high level of musicianship in the singing (and in the terrific onstage band) but also the unembarrassed charm of the performers, even when they are clambering over the customers, mussing up their hair-dos and handing out flowers and invitations to a be-in ("bring something to suck!").

Will Swenson's bestial Berger – you couldn't say he was a ham Berger – exudes a rugged charm even when mooning bare-bottomed at the audience. He has the dark good looks of Oliver Tobias, who played the role here, and doesn't seem to be "acting" at all. There are some great voices as well as his, notably Sasha Allen's gorgeous Dionne, who take us back to the Age of Aquarius and Darius Nichols's Afro-wigged Hud with a big creamy bass.

Did Hair change anything? Not really, though in pre-dating Tommy and Jesus Christ Superstar it pointed the way for rock music in theatre, a path virtually ignored by the theatre ever since (with the exception of Rent and last year's Spring Awakening).

It is, sui generis, one of the great musicals of all time, and a phenomenon that, I'm relieved to discover, stands up as a period piece with as much vitality and appeal as, in their own way, do No, No Nanette and The Boy Friend.

To 8 January (020 7907 7071; Hairthemusical.co.uk)