I have actually been present at the
recording of an episode of this wonderfully funny example of
British comedy. Some of the rounds not mentioned above include:
Trivial Hairsuit: a game in which the panellists have to answer questions on the subject of hair.
Limericks: celebrating the limerick that put the Irish town of Five Line Nonsense Poem on the map.
Name That X: Following the popularity of the show Name That Tune come the rounds, like Name That Motorway or Name That Novellist, where you have to name things other than tunes.
Just a Minim: Named after Nicholas Parsons' famous show, Sale of the Century (notice the sarcasm again). You have to sing a song without repetition, hesitation, deviation, or repetition.
There is also a round (I forget its name) in which you have to sing a song backwards. Given the abovementioned propensity for sarcastic titles, it may be called 'Backwards Singing' or something similar.