For those feeling wistful about "Little Britain" - maybe find some U-Tube or similar of old Dick Emery sketches, and you'll likely see pretty much the same material?!
There was a recent thread about The Good Wife (just a fantastic show, with courtroom stories and a side-show lampooning the American political system -- and a couple of terrific British actors) - presently being repeated on '5 USA'.
On other channels showing reruns you can find Rising Damp, Till Death (& its spin-off), Open All Hours, Duty Free, Dinnerladies, and other sitcoms when they had a working 'com' element!
Downton Abbey has I believe repeats showing in the afternoons, and we recently saw (quite by accident) a few minutes of Lark Rise to Candleford & Cranford, both being rerun. The original BBC Maigret series recently finished being rerun on the Talking Pictures channel (but it will surely reappear before too long!), and the same channel has Marker on the go, and the Cremer (French) version of Maigret.
Channels like Gold or Drama (etc) almost always have the likes of Allo Allo or Only Fools on the go, the other week His Nibs was changing channel and accidentally hit the Batman & Robin section of that episode, still far funnier than any modern alleged sitcom.