I've heard Bill Murray say how the unscripted format is the thing that really does get him out of bed in the morning with a spring in his step and a ditty on his lips. Our six brave folk from The House of Improv company, onstage at the blank, black space of the Michael Pilch Studio for the opening night of their Death By Murder: An Improvised Murder Mystery, naturally lack the professionals' experience (though two of them have three years of experience to fall back on. The others are novices). But they have youth on their side; supple, quicksilver youth. Vital, so you'd think, for the snappy repartee and instant reaction, though it's a sobering circumstance that in March last year at the National Theatre, four actors in their 70s and two in their 80s went on stage every night for a fortnight, each time creating a new show from scratch.

I've seen improv where the players have arrived with prepared backstories for their characters. Director and producer Jack Lawrence, with his colleagues, has taken the tough route to glory in that narrative, location and characters are all assigned ad hoc and by lot by the audience; more than fifty of us on this opening night. This is flying – or here gurgling – by the seat of the pants since chance decrees this murder is to be perpetrated aboard a submarine (a mountain top and zoo having been discarded) by means of a length of lead piping upon a victim unknown. So our six jolly tars lined up, reputations and possibly sanity on the line, simmering with energy and perhaps braced, too, for disaster. For the first round they strutted their stuff solo, relying on nothing but one costume prop picked from a row of hangers, a bit of musical accompaniment from the keyboard player, and such wit as nature had supplied and six intermittent weeks of practice had supplemented.

Thus we left port to the sound of twittering pipes with The Dragon (Will Jefferson), dived deeply with J-Swag (Rick Stevenson), bumped along the seabed with Dr Steve Twinkletoes (Jack Lawrence), upped periscope with Fifi le Fou (Sofia Castelló), scraped away the barnacles with Dimitri (Emma Hinnels) and pumped out the ballast tanks for surfacing with Twinkletoes (Eliza McHugh). Solo spots were succeeded by mix-and-match duets and then a brief ensemble line-up leading to the culminating crime. I say 'culminating', but in truth, I'd all but forgotten the murder wrapper until it was abruptly sprung on us at the end when a body crashed to the ground and we were invited to shout for the villain's identity. Was this Mystery a Hitchcockian MacGuffin with which to tantalize us?

So what was the overall standard, and how did our six perform? The audience plays a major part here, of course. This was no bear-baiting, bull-badgering arena à la Amused Moose Club in Soho, its stand-up comedy competitions predicated on a crowd that bays for blood. This was leafy Jowett Walk, and the student groundlings all around me were civilized and primed to laugh. The nigh-on 90 minutes running time is a fair length of time to fill, and I detected a slight drop in comic invention in the last 15 of those. But overall I thought they were terrific, sharp wit speckling the generous humour, and displaying astonishing aplomb. This is acting and thinking and reacting in the raw, our six stripped bare before us of all but their clothes.

Will Jefferson's Yorkshire Dragon was ducky in pink and black chiffon scarf but a nugget of blunt, Yorkshire grit. His was the creation that best managed some character development. Rick Stevenson was a smooth, imperturbable J-Swag, lightning-fast on the draw but dainty with little steps; and alive to the joys of analogy: 'Take a cruise ship with a tap on it and stick it under the water.' Sofia Castelló's Fifi le Fou was a stickler for on-board etiquette: 'Got to do things properly', and outraged by undersea hygiene malfunction: 'There are plenty of bacterial colonies in the toilets!' Jack Lawrence's Dr Steve Twinkletoes: 'I'm a married man... a doctor of bubbles' gave us a threnody on sexual frustration and aeration, and was notably nimble in reversing away from verbal cul-de-sacs.