Connor was born in Highbury, Islington, London, the son of a naval petty officer who organised concert parties.

During the Second World War he served as an infantry gunner with the Middlesex Regiment, but continued acting by touring Italy and the Middle East with the Stars in Battledress concert party and ENSA.

The full cast autographed the programme, suggesting a final performance for the concert party, with Kenneth signing it "All the best Ken Connor".

While waiting to be demobbed in Cairo, Connor received a telegram from William Devlin asking him to join the newly formed Bristol Old Vic, where he gained a solid grounding in the classics.

His most notable performances there were as Chaplain de Stogumber in Saint Joan and Dobchinsky in The Government Inspector, which starred Alec Guinness.

He starred in the revue One Over The Eight (1962), at the Duke of York's Theatre, the original London West End production with Frankie Howerd of the Stephen Sondheim musical A Funny Thing Happened on the Way to the Forum (1963), as Hysterium – and directed the show when it went on tour – The Four Musketeers (1967), with Harry Secombe at the Theatre Royal, Drury Lane, playing King Louis XIII, and the revue Carry On London (1973) at the Victoria Palace.

Between 1971 and 1973, Connor joined Dad's Army stars Arthur Lowe and Ian Lavender in the BBC radio comedy Parsley Sidings.

and he also appeared in the episode "Sense and Senility" of Blackadder the Third in 1987, alongside fellow veteran comic star Hugh Paddick.

His final TV appearance, as Mr Warren in The Memoirs of Sherlock Holmes episode The Red Circle, was broadcast posthumously in 1994.