This. So much this. I am so sick of seeing Lilley lauded as the next great Australian Thing. I fucking loathe all of his shows, they’re cringeworthy.
Citizen Smith
Steptoe and Son
The Good Life
Yes Minister
The Likely Lads
Man about the House
Chelmsford 123
Da Ali G Show
Bo Selecta
Brass Eye
The Day Today
Dear John
Extras
Hi-De-Hi
Hitchhikers Guide to the Galaxy
I’m Alan Partridge
Knowing Me Knowing You with Alan Partridge
Open All Hours
Can’t think of anything to add just now.
So far as Summer Heights High is concerned, I don’t get it…but my three teenage children who enjoy Monty Python/Blackadder/Catherine Tate etc love it.
My pick for additional interest is the Australian comedy “The Games” which is played as dry deadpan satire. The genius behind it is New Zealander John Clarke. If you want a taste of this dry type of humour, check out The Front Fell Off (which actually happened).
For the radio-minded if someone hasn’t mentioned The Goon Show, I wish they wouldn’t. 
You found what, now?
Sorry, Britishism. I mean old-school, downmarket, mass-appeal humour. The type you might encounter at a British seaside resort or holiday camp (such as Butlins, whose entertainers/MCs/general fun-enforcement agents are or were known as redcoats). Often delivered by cheeky chappies from “up north”.
Have been watching this list grow and grow and waited to respond because it seems we have fairly similar tastes; here’s my reccos that haven’t been offered up yet:
League of Gentlemen - oddball comedy, fairly gross and very very wrong
Alan Partridge - both series, lovely stuff.
Shooting Stars - awesome madcap panel show with Reeves & Mortimer.
Fonejacker - prank call show, but much more.
Skins - teenage comedy/drama in Bristol. Drugs/sex/love… but handles some very heavy issues for kids in the best way I’ve ever seen, and remains entertaining.
BoSelecta - part real part surreal, guy is a celebrity chaser and does weird impressions with masks on… worth it for the Little Bear and Marilyn Manson sketches alone.
And for the record - I agree on GreenWing. Pretty much the best British show I’ve seen from my perspective. Different, engaging and hilarious.
Holiday camp? Is that like a camping ground? Ours don’t come with entertainers, just wildlife.
[edit–]
Having done a bit of googling … Wow, we don’t have anything like that here … a fenced-in resort full of drunken vacationers … So a holiday camp is something like a carnival as executed by the Third Reich?
Yep. Exactly that. They became big in the 1950s and in fact one of the comedies I mentioned above - Hi-De-Hi - is set in a 1950s holiday camp and gives a good flavour of one. I never found it particularly funny myself but it was very popular so others may like it.
Filthy Rich And Catflap (the spiritual followup of young ones).
Q5/6/7/8/9/Theres a lot of it about - Spike Milligans shows, predates Python and Inspired it.
Absolutely (please please pick up the dvd for a song, its my favourite)
The Comic Strip Presents (Dirt cheap for box set of all episodes).
Fist of Fun/This Morning with richard not judy
On the Hour (radio version precursor to The Day Today)
Spaced
Avoid
Bottom (Avoid this if you liked Young ones etc, its same joke over and over)
Happy Families (First thing Elton did after Young Ones)
Bo Selecta, appalling crap
Heh, I think you’ve about got the idea. The traditional holiday camp is very much a thing of the past (although I see Butlins is still going, one would hope in a less regimented style). You are not the first person to see parallels between holiday camps and concentration camps :D.
I don’t like the sound of these 'ere boncentration bamps.
You’ve probably seen them, but maybe not, since they’re once-yearly: The Big Fat Quiz of the Year. It’s like a celebrity pub quiz night, covering news of the previous year, hosted by Jimmy Carr. It’s fun to see how many things you can answer yourself, since British news often doesn’t make it over here.
Plus, the celebrities are all very witty, and make lots of hilarious comments. My favorite of all of them (so far) was 2006, when Russell Brand and Noel Fielding were teamed up. They didn’t get too many answers right, but their wrong answers were very entertaining.
Berry and Fulcher’s Snuff Box.
Strangely repetitive. Oddly musical. Just weird. But quite good.
The Goth Detectives.
If In the Loop is anything to go by, The Thick of It looks like it would be pretty good.
Dave Allen At Large.
There are worse things to waste your life on than British comedy.
Believe Nothing, with Rik Mayall as an Oxford Professor. I remember it as having a mixture of highbrow and lowbrow humour.
‘Are you being served’ is on comedy central at the moment. I haven’t seen it.
'allo allo is the only other one that I can think of at the moment. Haven’t seen much either.
Has anyone mentioned Nighty Night yet? Just going by what you love (Peep Show, Green Wing and the like) this very dark comedy could be right up your street. It makes me want to hide under the sofa whilst biting on a pillow, but I love it: Nighty Night (TV Series 2004–2005) - IMDb
It is. it’s marvellous.