I saw this post and was going to nominate Mark Heap (Brian) from Spaced and, lo and behold, the last post was for exactly the same character.

Arthur from On The Buses whose facial expressions and dryness in delivering his put-downs to Olive were superb.

Great one-liner from him comes when Olive is cooking the dinner and Stan says:'Come on Olive what's in the oven.'
Camera pans to Arthur who says under his breath:'Well it isn't a bun I can tell you that much' before hiding behind his newspaper.

Spudgun in Bottom.

Denzil OFAH.

Sue- Gimme Gimme Gimme

Darren- The Royle Family

Rene's Mother In Law 'Allo 'Allo!
More I will think of them later

There are so many great supporting characters in British sitcoms. Some of my favourites:

Officer Crabtree and Lt. Gruber from 'Allo 'Allo!
Smiler, Wally Batty, Wesley, the policemen, and Eli from Last of the Summer Wine
Trigger from Only Fools and Horses
Owen and Jim from Vicar of Dibley
Onslow and Daisy from Keeping Up Appearances
General Melchett and Captain Darling from Blackadder

Cheryl The Royle family
Howard LOTSW
Frank Vicar Of Dibley
Marlene OFAH.
Blakey OTB

More to come