In the 1960s, he rose to prominence in the role of Alf Garnett in the BBC television sitcom Till Death Us Do Part (1965–75), created by Johnny Speight, which won him a Best TV Actor BAFTA in 1967.

Mitchell's other film appearances include Three Crooked Men (1958), Carry On Cleo (1964), The Spy Who Came In from the Cold (1965), The Assassination Bureau (1969) and Norman Loves Rose (1982).

He held both British and Australian citizenship[2] and enjoyed considerable success in stage performances in both countries, winning Olivier Awards in 1979 for Death of a Salesman and in 2004 for The Price.

[9] Richard Burton's description of the acting profession had convinced him that it would be better than completing his chemistry degree and so Mitchell attended RADA for two years, performing in the evening with London's Unity Theatre.

[10] He also had roles in The Avengers in addition to many ITC drama series including: William Tell, The Four Just Men, Sir Francis Drake, Danger Man and as a recurrent guest in The Saint, as in the second episode of the first season, "The Latin Touch" in 1962, depicting an Italian taxi driver.

[9] Mitchell's cinema début was in Guy Hamilton's Manuela (1957), and he began a career of minor roles as sinister foreign agents, assisted by his premature baldness and facility with Eastern European accents.

(Richard Lester, 1965) and played leads in All the Way Up (James MacTaggart, 1970), The Chain (Jack Gold, 1984), The Dunera Boys (Ben Lewin, 1985) and Foreign Body (Ronald Neame, 1986).

[9] In 1965, Mitchell was cast in the role for which he became best known, as the Conservative-voting, bigoted cockney West Ham United supporter Alf Garnett in a play for the BBC Comedy Playhouse series, broadcast on 22 July 1965.

Other small screen roles included a 13-episode series, Men of Affairs with Brian Rix (ITV, 1973–74), based on the West End hit farce Don't Just Lie There, Say Something!

In 1991 he starred as Ivan Fox, a Jewish atheist from London living in Belfast in So You Think You've Got Troubles, a BBC One comedy series written by Maurice Gran and Laurence Marks.

He also sang briefly in the film Till Death Do Us Part and played Alfred Doolittle on the studio album of My Fair Lady, Music Hall Songs, songs of the First World War, and other recordings such as The Writing's on the Wall, from 1967, on CBS, all in the Alf Garnett persona, were released in LP and 45 rpm single form, too, in Britain and Australia.

In 2008, at the age of 82, Mitchell was performing alongside Ross Gardiner at the Trafalgar Studios, in London's West End, as a retired dry-cleaner in Jeff Baron's portrait of Jewish-American life Visiting Mr.

[20][21] In 1976, Mitchell's one-man show The Thoughts of Chairman Alf won the Evening Standard Theatre Award for best comedy in London's West End.