You might not guess it from looking at this bunch of brightly dressed characters, skating haphazardly around Alexandra Palace ice rink in London with an armchair in tow, but in just a few days they will attempt to put on what is surely a theatrical first: a two-hour comedy stage show on ice. About global warming. And Stalin.

“I don’t know what will happen, but it will 100% be entertaining,” says Adam Larter, the founding member of Weirdos Comedy Club, who wrote Tony Law and Friends in the Battle for Icetopia. That seems a safe bet: the project is a collaboration between Law – a cult figure on the alternative comedy circuit – and Weirdos, both of whom have form when it comes to anarchic, seat-of-your-pants live comedy. The former embarks on wild flights of time-travelling fantasy during his live shows, the latter built a cult audience through their annual charity pantos, which have tackled everything from feminist mermaids to war epics revolving around KFC’s Colonel Sanders.

Still, at this late stage, there does appear to be one not-so-small problem when it comes to staging a theatre show on ice: Law has badly injured his knee. So much so that he can barely walk without howling in pain when I arrive at their rehearsal at this London ice rink – hence the armchair on the ice to save him having to skate. Law also admits that he hasn’t learned any of his lines yet. And the costumes – giant moose heads – are so heavy the cast are finding it hard to skate in them. Also, nobody seems entirely sure of the plot. Or if the microphones will work. Hang on, did I say there was just one problem?

To make matters worse, Law has foolishly agreed to take on a project almost as difficult as staging a two-hour comedy show on ice: guiding a Guardian journalist with no sense of balance around the ice as he attempts to conduct an interview. And so, as we wobble around together, Law explains how the play came about.

“I used to tease my friend Tim Minchin about how I was much funnier than he was, and how the only thing he had going for him was musical genius,” says Law, grabbing my hand before I smash into the sides. “Then I realised I had my own completely useless skill: ice-skating.”

Growing up in Canada, Law played ice hockey to a decent standard, but it wasn’t until he met Larter that his dreams of ice-based comedy grew into a full-on theatrical performance with a plot revolving around printing presses and polar bears. Polar bears? Yes, even after having it explained to me several times, it’s still hard to get a grip on the storyline …

“One character is a combination of Phil Collins and Donald Trump, captured in foam form,” explains cast member Helen Duff in the cafe after rehearsal. “I’m a cheese grater!” pipes up associate producer Bob Slayer. “It’s mainly nonsense,” admits Larter. Law jokes about how stupid it is for him to be taking part in this kind of freewheeling, DIY production at his age, but in truth it’s probably the most sensible time in his career for him to be doing so. It was only two years ago, after all, that he gave up drinking and started to hone his act.

“I was a classy alcoholic,” he says. “Top drawer. I would drink a lot. I’m not bragging, because of the lives I hurt, but I drank more than you’d believe.” What would a play on ice have been like if he was still hitting the bar? “Bloody,” he says. “I can’t imagine it would have happened, to be honest. It might have been interesting but it wouldn’t have been as nice. This has got joy and love and animals in it.”

Still, taking part has not been for the faint-hearted. Rehearsals take place on weekend nights, after the venue’s ice disco finishes around midnight. It’s the only time the rink is available. Then there are the technical difficulties: the lack of a backstage area, for instance, and the huge stage, which means painting scenery takes for ever.

“It goes against how you do live comedy shows,” says Matt Highton, a Weirdos member since they formed in 2010. “Normally, your urge is to move towards the audience. But you can’t do that here – because the audience’s view would be blocked by the ice hockey sin bins!”

You might wonder who is responsible for green-lighting this unlikely spectacle. Turns out the answer is a sensibly dressed, middle-aged man called Jeremy Walton, who has managed the ice rink for 27 years. “I just thought it was great, an unusual idea,” he says. “I hope they make a success of it.”

“That’s the sort of attitude you wish you heard more often in the theatre world,” says Law. “They clearly have a track record here of going, ‘You want to do what? Yeah, we’ll give that a go!’”

He’s not kidding: last year, Walton booked Vanilla Ice on Ice, a show so ridiculous that even Vanilla Ice himself decided he couldn’t go through with it. “He cancelled due to poor ticket sales,” says Walton. “So these guys are going where Vanilla Ice wouldn’t dare!”