In an era in which it is now an annual tradition for the US streaming giants to put out bland paint-by-algorithm holiday movies, there is something rather satisfying about the oddball British Christmas stand-alone special. The ingredients tend to be as follows: appearances by the year’s favourite comic actors; niche cultural references, with or without cameos; a wittily biting but heartwarming script that preferably leaves the viewer weeping into their Baileys.

In many ways, Finding Father Christmas hits all those notes, if never quite fulfilling its potential. It follows 16-year-old Chris (Bafta-winner and total delight Lenny Rush), who still believes in Santa despite being in the middle of his GCSEs. Three years after the death of his mother and with Chris still writing letters to the north pole, his concerned dad and depressed postman Nicholas (The Inbetweeners’ James Buckley) decides it’s finally time to have “the talk”.

Crunching the numbers … Stephen Fry in Finding Father Christmas. Photograph: Tom Martin/Channel 4

Nicholas lays it bare. Santa’s sipped whisky. The snow on the roof. The reindeer tracks. All done by him. But the show would be very short if Chris believed his dad, and so he embarks on a mission to prove him wrong and discover the science behind the magic, aided by his lovably eccentric cousin, Holly (Ele Mckenzie), and a range of experts.

The USP is that said experts are real-life scientists and thinkers playing themselves: Prof Hannah Fry, Dame Maggie Aderin-Pocock, and, for reasons I don’t quite understand, Jason Fox from SAS: Who Dares Wins. Everyone involved is a good sport as they use physics to explain how Father Christmas does the seemingly impossible in just one night. But it is national treasure and mediocre faithful Stephen Fry who steals the show.

Having stalked him via a tipoff by the local Santa (a guest appearance by People Just Do Nothing’s Asim Chaudhry), Chris, Holly and super fan Nicholas find themselves in Fry’s front room being given a full-blown presentation weighing up the logistics of Christmas Eve, complete with a chalkboard and equations. (Look out for the press clippings framed above Fry’s downstairs toilet.)

There is a sweet side plot in which Nicholas tentatively takes a step back into dating with Miss Bailey (Rochenda Sandall), Chris’s science teacher who lives across the road. But there would surely have been more depth to the characterisation if Chris had gone on the journey of discovery with his dad rather than his cousin. Buckley and Rush are a wonderful pairing who clearly could have carried it off, with Rush showing the same easy chemistry that saw him shine with co-star Daisy May Cooper in Am I Being Unreasonable? I find myself wishing the script had been returned around February with a note from Channel 4 bosses asking to turn it into a two-hander, in a similar vein to 2018’s pathos-filled Click & Collect.

The TV equivalent of a Christmas buffet … Asim Chaudhry as Santa with Ele McKenzie as and Lenny Rush as Chris. Photograph: Big Talk

Instead, we’re given multiple characters we never really get enough time with. There’s a fun scene reminiscent of Paddington where Chris and Holly break into a warehouse to discover the truth about Father Christmas, but Taskmaster’s Greg Davies is criminally underused as the big man himself, other than a quick joke about air fryers as dated presents. Similarly, there’s a nice running gag about Royal Mail (you can imagine legal action starting over the claim that they shred children’s letters to Santa), but Nicholas’s unhappiness at work doesn’t get the chance to be properly explored. We do, however, get some time with Holly and her podcast without any explanation of her role in Chris’s life or why she is keen to commit crimes for him. It is the TV equivalent of a Christmas buffet. A nice sausage roll there, a pot of Pringles here. But you can’t help wishing you were sitting down to a full roast dinner.

By the end, I simultaneously have the feeling it is going on too long (call me anti-expert but after physics has been explained in terms of Santa’s movements once, do we need it again and again?) and also could do with an extra 15 minutes. The loss of Chris’s mum is covered briefly in the first and last five minutes, but some exploration in the middle would have given the whole thing more emotional punch. As the credits roll, I am not crying into my Baileys. Perhaps I’m dead inside. Perhaps I started drinking this morning and fell asleep in the third ad break facedown in a panettone. Perhaps – and I’m going with this option – there needs to be a part two next year to fill in some of the blanks.

I vote Chris and his dad spend Christmas Eve with Davies’s Santa, ideally with a post-watershed liberalism to expletives. The physicists can come along for the ride (if they must).

Finding Father Christmas is on Channel 4 now.