Grandma's House, BBC Two

There are many for whom Simon Amstell can do no wrong. He is clever, he is funny, and he fronted Never Mind the Buzzcocks. What’s more, although his appearance suggests a cute, geeky vulnerability, his exquisite sarcasm can skewer the most inflated, the most inured of celebrity egos. The egos queued up to be guest panellists on that cool music quiz, only to get shot down by some clever, insightful putdown.

But what if Amstell goes home to bed every night feeling really bad about being so mean to people - people who haven’t even offended him personally, but who simply present themselves as a cheap shot?  Every week we had pop personalities lining up with the audacious idea that they just might be the ones to escape the inevitable. They tried to look effortlessly cool, but were betrayed by their puppyishly eager faces: clearly they wanted to be Amstell’s best friend. And Amstell seems to have developed a conscience about this.

So, in 2007, with collaborator Dan Swimer, he created a spoof Imagine, in which Alan Yentob interviews him and neatly turns the tables: Yentob exposes Amstell as a right old meanie, while Amstell’s defensive responses sound self-justifyingly hollow. The piece was terribly self-indulgent, and not very funny (Yentob can’t act, even as himself, and ditto Amstell). But it obviously gave Amstell the idea for creating a sitcom in which he again appears as his same-name alter ego.

In Grandma’s House, also co-written by Swimer, Sitcom Simon wants to give up TV and do something meaningful with his life. Meaningful without the mean. He suggests that he might become a Buddhist. “People congratulate me for being mean,” he wails. “It’s not mean, it’s cheeky,” his sitcom mum counters. “You’re a cheeky chappie.” Sitcom mum Tanya (Rebecca Front) shamelessly basks in the glory of her TV son’s TV fame. “You’re on television. What more do you want?” she asks.

The set-up, with its regular family gatherings at grandma’s house in semi-detached, nondescript suburbia, is typical sitcom territory. There’s Gran and Grandpa, mum, auntie (your archetypal childhood auntie: all fluffy moustache and bad hair), irritating nephew, plus mum’s new man, Clive, who thinks he’s funny, but obviously isn’t. Post-modern telly sitcoms are hardly new, so all the self-referential stuff that underpins much of the initial humour gets a bit thin after five minutes. And the script, like Amstell, is leaden. To be honest, he just looks seriously bemused throughout. And he delivers his lines with all the expressiveness of one who’s had a faceful of Botox. Except between the brows. He frowns a lot: when he wants to look aghast he raises his brows, and when he wants to look embarrassed he lowers them. Thankfully, other cast members acquit themselves well.

I’ve heard that episode two manages to settle into its stride. But only a die-hard Amstell fan would wish for a second helping.