...check out Inside No 9, an anthology series by Shearsmith and Pemberton, the two League members who kept the black comedy fire burning after the group semi-retired. It's more about clever twists and plot structures than being a straight comedy, but a lot of the episodes are really great.
They also did a more serialised League-like series called Psychoville, which is an acquired taste but has some good stuff in it. It also stars Daniel Kalluya before anyone knew who he was.
Most things Armando Iannucci or Chris Morris have been involved in together or apart are fantastic, though their stuff can be topical and involve UK cultural references that might not travel.
Re: Bottom, it's quite deliberately as stupid and childish as possible, it has some great stuff though: