Sebastian “This IS ‘The Other Place’!” Cabot
I can beat that (citing an out of date actor, I mean). Ronald Colman. He was always a gentleman but never an upper class twit. He was intrepid but not foolish; romantic but not soppy. I mean his characters of course.
Or Sir Wilfrid Hyde-White. Sometimes more of a caricature, if that’s what the OP had in mind, but always supremely English. Played Colonel Pickering in the movie of My Fair Lady.
Brian Gordon’s alive?! Blessed …
Brian Blessed
Mr Bean
Captain Mainwaring
What about Rex Harrison? Or, for that matter, Leslie Howard? They both played Henry Higgins, in My Fair Lady and Pygmalion, respectively.
How about John “Polovetsian [sic] Dance No. 2” Williams?
Arthur “I’ll be about me duties, now, sir.” Treacher?
David “Mr Banks” Tomlinson!
1930s and 40s character actor Henry Stephenson as a kindly old gentleman.
That’s who I came here to say (since I’ve been watching Family Affair reruns on Hulu 
)
Mine have all already been mentioned – Cabot, Caine, MacNee, Niven…
Captain Pugwash
Master Bates
Seaman Staines
Roger the Cabin Boy
So…Joey Barton?
Michael Kitchen.
Jim Carter of Downton Abbey fame.
McGoohan was Irish. His accent in Danger Man is unmistakable.
Phileas Fogg from Around the World in 80 Days (who was played, in the Michael Todd version, by David Niven, already listed above)
And I omitted Sean Connery because he’s Scottish! :smack:
If I might tweak the premise of the thread a little, how about Victoria Coren Mitchell? Seems to have that touch of haughty disdain that that the English do so well.
I can’t see him without thinking of him playing Deja Vu in Top Secret!
And the cross-dressing actor in Shakespeare in Love, or the Goering-like henchman in Ian McKellen’s neo-Fascist Richard III.
Joey Essex.
And by Pierce Brosnan in the TV version … but I believe he’s Irish as well. 