This has been my 20th Edinburgh season as a journalist. You might think that I’d pretty much seen it all by now. So did I, but one should never underestimate the capacity of this phenomenon to surprise and delight. I’ve mentioned before that in recent years a number of shows have offered themselves to perform in your own house or flat; this week, however, I experienced another kind of personal presentation.

Showstopper! – The Improvised Musical has been performing on the new George Square Fringe campus dedicated to musical theatre. The company’s artistic director Adam Megiddo contacted me several weeks ago to ask me to write a review for them. Not a review of their show… not quite… They planned, for their final batch of performances, to invite a critic each night to present the company out of the blue with a review of an imaginary musical, which they would then turn into reality.

It was too deliciously bonkers to resist. Almost immediately a line popped into my head: “The chorus line of roller-skating rabbis was a genuine coup de théâtre.” Dare I go that far? By way of research, I went to see one of the company’s earlier performances, during which they took ideas from the audience. The cast of six, gently nudged by Dylan Emery, created a semi-plausible musical about Norfolk/Suffolk feuding around an age-old bell-ringing competition, and somehow managed to fit into this framework a daft reggae number. Their Bob Fosse-style finale was breathtaking, with Megiddo sliding on his knees to the front of the stage to cue his comrades in. That night I realised that, in my fantasy review, I could get away with anything. I let my most wicked impulses off the leash.

The result was an FT-style article describing a musical about a love triangle set against the backdrop of the 2008 Lambeth Conference, in which personal emotions mirrored the tensions threatening to pull apart the Anglican communion. The show was entitled Schism! (exclamation mark mandatory). How much more awkward could I be? “The book shows astounding assurance, considering that this is Mark Ravenhill’s first foray into commercial musical theatre,” I wrote, and then trumped that with the bad-taste “In a touching tribute to an old friend, the lyrics to one number have been worked up from notes found among the papers of the late Sarah Kane.” I threw in some world music elements, a brace of bad-pun titles and even a couplet of lyrics. I was being a real git, but not – I hoped – an unhelpful git. I was not asking the impossible, just the very, very improbable.

On Wednesday lunchtime I met up with the company’s mentor and guest director Ken Campbell, who explained how he envisaged that evening’s performance working. Suddenly panic struck: it seemed that Campbell expected me to “call” every scene, specifying circumstances, tone and musical genre. I spent that afternoon, between the other shows I attended, frantically sketching in ideas. An Act One finale called “Sunday Fucking Sunday”? No problem. Another number that sounded like “Goth Boublil & Schoenberg”? Piece of cake.

In the event, my scribblings were unnecessary. I didn’t dare look at the company as I read out my challenge, but once they had started, they kept the show running, with occasional direction from Campbell and his lieutenant Josh Darcy (who had earlier demonstrated a remarkable approach to reciting Shakespearean soliloquies ventriloquially). Pippa Evans was touching as a female bishop, Nathan Taylor staggering as the deacon she loved but who had eyes only for hardline conservative prelate Sean McCann, the company’s leading spoken improviser. In fact, when they got their teeth into the Sarah Kane pastiche scene, which rapidly developed into a blood-and-sperm bisexual threesome, McCann at one point howled, “I’m an alcoholic for the love-scotch of your loins!” and after the show was astonished to be told that he had done so. It doesn’t sound very Kane-esque, but it’s virtually the only line from the scene that is quotable in a family paper. And yes, they were interrupted by a trio of roller-skating rabbis; as a bonus, an Argentinian imam also showed up.

The big finale “We All Must Wholly See” was far more united than the Anglican Church, and after the deserved applause had died down I picked my jaw off the stage where it had lain for the previous 40 minutes in fascination, horror and childlike pleasure that all this had been my personal command performance. It was the show of my dreams, if I had been ingesting vast amounts of cheese.

Written for the Financial Times.