There have been plenty over the years. Some that spring to mind are:
Richard Wyler (Stapley) made quite a few - The Bounty Killer being the best
Sean Connery, Jack Hawkins, Honor Blackman, Eric Sykes - Shalako
Susan George - Sonny and Jed
Kenneth More (and a bunch of support players) - The Sheriff of Fractured Jaw
John Steiner - Tepepa and Mannaja amongst others
Terence Stamp - Young Guns
Joan Collins - The Bravados and The Cry of the Wolf
Jeremy Irons - Appaloosa
John Mills - Chuka
All the Carry On mob - Carry on Cowboy
Angela Lansbury - A Lawless Street (with Randolph Scott)
Victor McLaglen - Fort Apache, She Wore a Yellow Ribbon, Rio Grande
McLaglen is often mistaken as Irish because of his name and all the parts he played in John Ford's films but he was actually English and started his film career in London.
Despite playing 'English Bob' in Unforgiven though Richard Harris was Irish of course so doesn't really qualify.
I'm sure there are others I've forgotten for the moment.