This thread is just for British characters who are on American shows, not all English shows like Fawlty Towers and Are You Being Served? Unscripted shows can be included as I am putting a few on.

Mr. French (Sebastian Cabot)- Family Affair
Mr. Bentley on The Jeffersons- He is often the best part of the show. Episodes without Bentley aren't as good.
Daphne Moon (Crane)- Frasier
Simon Moon- Frasier
Gertrude Moon- Frasier
Mr. Belvedere
Maxwell Sheffield- The Nanny
Maggie and Hal Conway- Mad About You
The Beast (Mark Labett)- The Chase. He seems more at home on GSN than ABC.
Anne Robinson- The Weakest Link
Alice (Sophie Lowe)- Once Upon a Time in Wonderland
Simon Cowell- America's Got Talent
Simon Cowell- American Idol

Mr. French (Sebastian Cabot) - Family Affair
Maurice (Maurice Evans) - Bewitched (not sure the character was intended to be British but the actor was)
Miss Naugatuck (Hermione Baddeley) - Maude

The character from Hot in Cleveland. She was one of the 3 ladies traveling from L.A. but had land in Cleveland.

Craig Ferguson as Mr Wick on The Drew Carey Show - he was CRAZY

just trying to thiink of some more British sitcom characters -

Geoffrey on Fresh Prince of Bel Air
Mr Belvedere
Maxwell Sheffield - although I thought Niles was funnier on the Nanny

Callum Blue as Mason on Dead Like Me
Charlize Theron as Rita Leeds on Arrested Development
Dave Thomas as Trevor Leeds on Arrested Development
David Cross as the Bluth's British nanny Phylidia Featherbottom (but it is really his character Tobias Fünke in drag - which everyone else is aware of but play along because he is actually doing the housework)
Jane Carr as Louise Mercer on Dear John

Mr French - Family Affair
Newkirk - Hogan's Heroes
Dr Bombay - Bewitched
Davy Jones - The Monkees

The Bugoloos