New venue. New enticement. In the undercroft of a vast but disregarded Bloomsbury church nestles the Museum of Comedy. The below-stairs space wears the heavy oaken lineaments of Victorian piety but the flagstones have been smothered with prim suburban carpeting, wall-to-wall. There’s a bar in one corner. Yes, a bar in a church. With prices high enough to make you take the pledge. The ecclesiastical shelves are crammed with books, magazines, scripts and photographs that summon up the ghosts of our comedy heroes. A big carved pew, centrally plonked, invites the worshipper to sit and read, let us say, the autobiography of Clive Dunn or the diaries of Kenneth Williams.

The sheer incongruity of this arrangement causes palpitations in the brain. A comic reliquary installed beneath a London minster is as weird as a stamp collection entombed in a gasworks or a museum of osteopathy placed on a roundabout or an archive of novelty egg-timers at the North Pole. The effect, as often with such shrines, is to create a distance, not a connection between the devotee and the object of veneration. Comedy is a warm, fleeting wraith and this scrapyard of physical paraphernalia excludes rather than conjures up its essence.

Next door there’s a tatty little parlour set up as a theatre with 62 rickety seats. Most of them complain loudly when being occupied. The forlorn stage has been assembled from a few palettes nailed together. A thick grey shroud serves as a backdrop. (In the summer I expect it’s somebody’s picnic blanket.) The lighting isn’t quite torches and candles but it’s close. The usherettes are gorgeous, matey and slightly indolent, which adds to the welcoming atmosphere.

The premise of Goodbye, The [After] Life of Cook & Moore is as muddled as the title. We’re in heaven. Or hell, perhaps. Or limbo? Peter Cook has been waiting seven years for his old mucker to snuff it and when Dud arrives in the hereafter he’s greeted with blasts of insulting mockery. The characters meander through their life histories while offering glimpses of their best-known pairings: the sweary Derek and Clive, and the whimsically erudite Cockney tramps. The material by Jonathan Hansler and Clive Greenwood is newly minted, and this points to something extraordinary. Cook’s oeuvre is pretty slender and yet his persona, and his vein of playful absurdity, is potent enough to inspire modern apprentices to create fresh work that is almost indistinguishable from the master’s. Few artists have generated such a tradition.

The play’s focus rests firmly on Pete, whose character is more forceful, dark and intriguing than his partner’s. Co-writer Hansler gives an outstanding but unstarry performance. He’s a relaxed, oblique, guileful actor who uses no trickery or imposture but steals noiselessly inside his character and animates his spirit for an evening. Dud, cheerfully done by Kev Orkian, is underdeveloped. He’s just a podgy dartboard on which Pete nails his anger, jealousy and pettiness. When Dud struck gold in Hollywood Pete dismissed him as a ‘sex thimble’ and yet he was desperate to emulate Dud’s success. He skipped over to LA to play an English butler in a flop sitcom and then slunk back to Hampstead’s pubs where he liked to complain that Johnny Rotten had stolen his deadpan estuarial delivery.

Both actors forget their lines occasionally and this electrifies the show. Pete and Dud themselves flirted with off-piste improvisations so when the thesps fumble their cues they literally become their subjects as they scramble to find a route out of trouble. The director Vadim Jean acts as prompt-caller. But instead of whispering a missed line from some discreet perch near the stage he bellows it out from a throne, commandingly placed, at the rear of the room. This informality suggests that the show isn’t so much a play as a ‘studio pilot’, in BBC parlance, namely a rough-and-ready version done with minimal props to help commissioning editors judge its potential as a TV show. Looks to me like the deal’s done.

The Separation is billed as a tribute to Ireland’s 1995 divorce referendum. Not quite. It’s a macabre sex comedy set 20 years ago with divorce as a central theme. Skilful marketing, therefore, not social analysis. We’re in a Dublin flat where forty-something Stephen has seduced a beautiful playmate half his age. Their semi-naked sofa romp is interrupted by the scrape of a key in the latch and the arrival of Stephen’s wife, whose existence he has omitted to mention to his panting lover. Stephen’s greeting, ‘sweet suffering mother of almighty fuck’, confirms that the Irish retain the world crown for swearing. As a slice of comic melodrama this 75-minute play works well enough until the closing moments, when Stephen reveals himself as a violent nutjob. This spoils his character and embitters a sweet and captivating confection.