Whose Line Is It Anyway?, London Palladium

At least half the audience for this live version of the short-form improv show, which was shown on Channel 4 between 1989 and 1998, couldn’t possibly have seen Whose Line Is It Anyway? when it was first broadcast, so one assumes they must have become fans via YouTube or rerun channels – testimony to the idea that good comedy is timeless and ageless.

The West End version of Dan Patterson and Mark Leveson's creation is an appealing melding of old and new. The acerbic and quick-witted Clive Anderson is back as master of ceremonies, and producers maximise his presence by giving him a 15-minute solo spot to open proceedings, with a script so smart and witty about (among many other things) Donald Trump, David Cameron and the EU referendum that one longs for him to do stand-up proper.

He introduced original performers Josie Lawrence, Colin Mochrie and Greg Proops, who have developed both a chemistry and an innate understanding of where the others may go with a joke, while making sure they get their own in too (there is always healthy competition in good improv). New to UK audiences are the equally quickly witted Brad Sherwood and Jeff Davis – regulars on the US version, which is enjoying a renaissance of its own. They are both outstandingly good, bringing a different, more laidback vibe – although, like Proops, they aren’t above throwing in an obvious sexual reference to get a guaranteed laugh.

It doesn't fall into the trap of becoming a nostalgia-fest Like sketch comedy, improv – even the best – can be a mixed bag; some games work better than others, and one section may pan out terrifically well one night and fall flat the next. But Anderson is an astute judge of when to buzz the end of a game, and all the old favourites (with exception of the props game) were here – including World’s Worst, Freeze Frame, Party Quirks and Hoedown – in a packed show lasting more than two hours where the quality only occasionally dipped (usually because the audience volunteers weren't up to snuff and there's only so much the performers can make out of their participation).

Highlights on the night I saw the show were Sherwood and Davis serenading a woman from the audience who works as an osteo-archaeologist (try rhyming that), Proops getting in an anti-Trump joke wherever he could, Mochrie as the Hollywood Director making the others play out a wilderness scenario in various film styles, and anything involving Lawrence belting out a song made up on the spot (to great accompaniment by the two musicians on stage, Laura Hall and Linda Taylor).

While Whose Line…? hasn’t entirely reinvented itself – and why would it? – neither does it fall into the trap of becoming a nostalgia-fest. This is a terrific night’s entertainment by performers who make a highwire comedy format look as easy as falling off a log.

• Whose Line Is It Anyway? is at the Palladium, London W1 until 19 June