Tom Stoppard's 1974 play Travesties has an exceptionally unreliable narrator at its heart. And goodness, how Stoppard revels in his unreliability. Essentially the story of Henry Carr's days as a young English consular official in Zurich in 1917, Travesties presents a moment in history where political, cultural and social fault lines collide. A lot of the events in the play are real but is Carr? Stoppard insists so (he says Carr's widow wrote to him after the premiere). But Carr's voice is undermined by the fact that he is narrating everything as a very senile old man. As Carr himself says: "I stand open to debate on all points except my height…"

With Travesties, then, Stoppard has maximum fun with us, history and theatre, something that Patrick Marber taps directly into with his revival. It's a completely bonkers, fast-paced, non-stop, roller coaster ride. And it's very, very, very funny. It's also quite difficult to keep up with and if you aren't familiar with some of the artistic movements, figures and events of the time, you may struggle. That said, Carr's remarkable time in Zurich brings him into contact with some fairly famous names – James Joyce, Lenin – so we're not talking oblique references here.

Book-ended by Tom Hollander's wild-eyed, mischievous and ageing Carr in his dressing gown and battered boater, the play begins with the consular official recounting his memories. These are then played out onstage as Joyce, Lenin and a key figure of Dadaism, Tristan Tzara cross paths because of their connection with Carr himself. Events stop, start, begin again, characters change and stories alter. Everything moves with the whim of Carr's memory.

"At least it's not clever nonsense," says Tristan Tzara at one stage in response to a rebuke about the point of Dadaism. And it seems obvious that Stoppard is trying to replicate the movement's playful, nihilistic, cut-up intentions before our very eyes. He takes a timeline, moves things about, changes them and makes us wonder where the truth lies. Is it in the story? In the work of art? Maybe it's all just made up.

Ultimately, the play is about the value of art, the artist and the importance of truth. And though they may sound like heavy subjects, they are treated in the most delightfully nonsensical way here. Stoppard takes the piss out of everything and anything, from Lenin's bald head and Joyce's limerick poems, to Tzara's general ridiculousness. Somewhere right in the middle, a production of The Importance of Being Earnest pops in to further confuse the hell out of everyone.

Hollander is pitch perfect as Carr, delivering Stoppard's beautifully crafted lines so they land with maximum hilarity. But the whole cast are superb to watch as they romp through Carr's mad history. Clare Foster comes into her own in the second half as the revolutionary librarian Cecily who suddenly does a sex dance in-front of Carr (another moment of fantasy). Freddie Fox occasionally over-eggs it as Tristan Tzara, but he times his dialogue brilliantly and riffs with Hollander exceptionally well.

Marber's production feels a little remote on the Apollo Theatre stage after a run at the more intimate Menier. But though Tim Hatley's labyrinthine set looks very static, it proves surprisingly flexible, allowing the actors to poke their heads, arms and bodies into view at unexpected moments.

Though there's no denying that this play is a heady treat, the only slight grumble I had was that very occasionally Travesties feels smug. But anyone who isn't dazzled by Stoppard's ability to make a work of art from complete human gobbledygook is missing something. And this superb revival does the piece absolute justice.

Travesties runs at the Apollo Theatre to 29 April.

Watch our interview with the cast of Travesties