In the many risk assessments of the possible consequences of Brexit happening on Halloween – lorry queues, drug shortages, street violence – scant attention was paid to a significant victim of its not happening: broadcasting specials timed to coincide with departure from the EU being forced to go out, even though the UK actually hadn’t.

The special Brexit edition of Little Britain, bringing David Walliams and Matt Lucas’s sketch show back to Radio 4, where it started in 2000, was at a double disadvantage. Having been denied its calendar reason for being, it also now found itself broadcast in the run-up to a general election, when the BBC’s already contorted attempts at political impartiality become even stricter.

So perhaps there were tougher sketches or punchlines that might have been included either if Brexit had happened or the election hadn’t. But, in the version transmitted, there was often a sense of EU references being shoehorned into scenes that could have been written when the show was on Radio 4 and then BBC TV, back in the early Blair years, and before Donald Tusk even became Polish prime minister. One joke required English universities to be teeming with leavers, the exact opposite of reality.

Admittedly, “Yeah but no but yeah but”, the mantra of Vicky Pollard, the show’s notoriously opinionated but clueless schoolgirl, could serve as a description of the progress of the various Brexit bills through the House of Commons. However, an opening sketch in which Pollard, addressing speech day at her old school, got politicians’ names childishly wrong (“Joris Bonson, Nigel Frog”) felt inadequate to the magnitude of the matter.

There, and elsewhere, the show ducked the possibility of exploring a “Little British” attitude among some leave voters. Marjorie Dawes, the racist runner of a slimming club, who is prone to finding the accents of foreigners incomprehensible, was omitted from the cast list for this special, which felt like playing safe.

We did learn that lonely homosexual Daffyd Thomas voted leave, though not for any of the reasons that led so many real Welsh people to do so, but because he feared that free movement of European homosexuals would remove his status as “the only gay in the village”. As with the catchphrase transition by which Walliams’ obstructive travel agent now blocked holidays on the grounds that “Brexit says no”, rather than the original “computer says no”, the gags were largely the usual ones against the characters, rather than attempting any more provocative topicality.

The most original sketch, in which a devout Brexiter was appalled to find herself owing her life to a transplanted organ from a remainiac, will be useful to historians of this period, in the way that newspaper cartoons are, as a reflection of the bitterness of the British culture wars at this time.

As the regular characters of the franchise included a Blairite British prime minister and his homoerotically obsessed aide, Sebastian, fans spent the episode assuming that the duo must feature, though unsure precisely how. They were sensibly kept until last, but got a fantasy sequence – featuring yet more of the show’s already queasily frequent wordplay about gay sexual practices – that gave way to Sebastian’s encounter with a badly impersonated Boris Johnson.

The series came back to radio rather than TV because, in production terms, sound can move faster than pictures. And, in making a link between Brexit sentiment and Little Britain’s characters, Radio 4 had the germ of an interesting idea. Finally, though, a documentary about the extent to which popular culture reflected the tension with the EU might have been more effective than a programme that, like so much of the BBC’s coverage of this subject, felt hampered by restrictive theories of even-handedness.