The first five(?) series of Red Dwarf, Blackadder, League of Gentlemen, The Fast Show, Harry Enfield and Chums, Blackadder, French & Saunders, The Day Today,Absolutely Fabulous were all pretty damn good.
Of the classics, you have Are You Being Served? The Young Ones, It Ain't Half Hot Mum, Some Mothers Do 'Ave Em, Not the Nine O'Clock News, Monty Python, Up Pompeii (Frankie Howard is probably one of the greatest unsung comedy genius), Kenny Everett and of course the Carry On series.
Bugger all since the millenium which has even come close though. Also, does Dame Edna count as British humour, or do the Aussies get it too?