Hair at the Gielgud is a wonderfully witty match of production and venue, with the portrait of the great actor, bald as a coot, beaming benevolently over the punters in search of the summer of love and long locks in Greenwich Village in 1967.

The “older generation” is on stage, too, in the shape of Claude’s parents, the army officer and Abraham Lincoln, who, needless to say, gets shot.

So it’s no surprise that the Broadway cast - the first time an entire musical theatre personnel has been transported, unaltered, over the Atlantic - is doubly keen to grab the young spliff-friendly vote: “I’d like to sit up there with you guys,” shouts Will Swenson’s charismatic Berger, “you’re higher than anyone down here!”

It’s a great virtue of Diane Paulus’ totally engaging Public Theater production that the innocence and unbridled high spirits of the tribe – sharing their love, peace and happiness around like a box of chocolates – are not tainted with cynicism or even silliness. The show is for real, but also locked in its period and aware of its own theatrical playfulness.

The main guys are the wild man Berger and the more reflective Claude, spending a last few hours in the Village before signing up for military duty in Vietnam. Unlike the recent Gate Theatre revival in London, there is no attempt to “Afghanistan” the action, and no need.

Hair, for all its faults in book and lyrics, is genuine social history in an Age of Aquarius that pre-dates all the modern war films, Aids, the horrors of drug abuse (turning on is like taking a warm bath, a miasma-like experience beautifully rendered in the music), even the green movement, though there is a prophetic blast of eco-friendly special pleading.

This revival also makes positive all the clichés and sloganeering by giving them a sort of Brechtian incantatory power, again much aided by Galt MacDermot’s score, which is both sensationally well sung and brilliantly played by the onstage band under Richard Beadle’s musical direction.

The first great rock musical turns out to be a one-off masterpiece in its deployment of blues, jazz, bass rhythms, brass riffs and flat out melodic anthems, paving the way, no doubt, for Tommy and Jesus Christ Superstar but absolutely on its own as a lexicon of the jargon, taboos and post-war high school rebellion that shaped and stamped a whole generation. And who says making love, not war, is a bad idea anyway?

Gavin Creel is a charming and sympathetic Claude, fully earning his right to sing my favourite of all Shakespearean settings, “What a piece of work is man”. His artfulness with the number is matched by Allison Case’s beautiful delivery of “Frank Mills” and the whole cast’s irresistible surge through the great opening and closing chorales, the last staged with a particular and characteristic understated clarity.

Joy is all the more unconfined for being so carefully contained. And, yes, you can get up on the stage and join in the dancing. I’ve been there, done that, got the T-shirt, but I enjoyed watching others give Sir John another friendly shove in his grave.