Occured to me that several of my favourite U.S. sitcoms use the funny device of an unseen character. Currently, Wolowitz's mother in Big Bang. Maris (Niles' wife) in Fraser. From re-run land, Lars (Phylis' husband)in Mary Tyler Moore, the doorman (Carlton) in Rhoda, Vera in Cheers.
But I can only think of two examples in British sitcoms... Mrs. Mainwaring in Dad's Army and Sheridan in Keeping Up Appearances.
Any others I have yet to see or have forgotten or is it actually a less-used plot/comedy device?