If you want to go proper vintage, I used to be quite fond of Whatever Happened To The Likely Lads. It's one of those mundane everyday life kind of things.
The Inbetweeners has a big following and I've seen bits that were quite funny and Peep Show-esque, though I've never actually watched it.
For non-sitcom comedies, definitely check out Chris Morris's stuff, esp The Day Today, Brass Eye, Jam. Some of them are a bit of their time, but still funny.
Also you might know it but Inside No 9 is really good. It's not strictly a comedy, but a really clever anthology show by Reece Sheersmith and Steve Pemberton from League Of Gentlemen. Their series Psychoville is worth a go as well, which featured this memorable scene:
A Smith would be a good one for this question, he knows his Brit comedy stuff.