As a kid who grew up in Australia you may be aware due to cultural and financial deficiencies we basically poached a lot of British tv.
The only podcast I listen to every week is the Weekly Planet Aussy duo of Nick Mason and James/Mr Sunday Movies, and yeah, part of their charm for me is the weird cultural overlap between Brits and Aussies of certain eras.
It's been mentioned before, but Porridge is absolutely worth checking out. A true classic, it had incredibly smart, quick witted dialogue, but it also had a socially critical context and a genuine character driven pathos. Like a lot of British comedy of those eras, there was a heavy dose of self-deprecating melancholy.
Culturally it's fascinating to watch now, as well, with the opening episode touching upon perceptions of sexuality, race, and religion. The non-straight is primarily used for the purposes of jokes, but there is no real mean spiritedness about it nor are they attacked, so it has a strangely liberal, equalising vibe to it.
Same with religion, with Barker's character suggesting the relatively innocent newbie should've said they were a Muslim or Jew simply for the sake of holidays and food exceptions, as opposed to C of E which gets you nothing...
It's about getting one up on the system, retaining a sense of self-identity, and so it's also quite existential as the characters mull over their mistakes and dreams set against the prison system and the society beyond. It also explores generational gaps, and plays up the disparate cultures and communities spread across the British isles, but also simply throughout England.
Whether it's funny or not to a given person is of course subjective, but it really was much more than just a comedy, and I personally find the best episodes still hit their mark in terms of pathos and social commentary several decades on, which is quite the feat.
On the other end of the scale (mostly), is The Fast Show, a very quickfire sketch show from the '90's. Given the format it's a scattergun approach, and I'd say most people will find a fair amount they don't particularly laugh at each ep, but the performances and characters are so good that, generally, it's always very watchable.
The 'black' painter---
And Dave Angel were two of my faves---
(I assume one or both might not work for some people depending region)
Like Porridge, it generally has an immense amount of humanising affection for the characters shot through it, though obviously it's a far more gag/catchphrase oriented series.