Watson's father was killed in Belgium in World War II. He was educated at Eton College and made his first appearance on stage whilst still a student at the Webber Douglas Academy of Dramatic Art at a matinee performance in memory of Ellen Terry at Hythe, Kent. After appearances in repertory, he appeared on the West End stage, including The Doctor's Dilemma and in The Rivals by Sheridan both at the Haymarket Theatre.
In 1963, he went to New York City to appear in The Private Ear and The Public Eye.
He played the part of the Art Editor in the BBC series Compact for some years.
He appeared in several films, including Operation Crossbow and The Grass Is Greener, in which he played opposite Robert Mitchum and Cary Grant.
He has a series of television credits to his name, most notably as Brigadier Arthur Maiford, M.C. (ret.) (but always known to the Larkins as "The General") in The Darling Buds of May (1991–1993); and George Frobisher in Rumpole of the Bailey (1978–1992).
He also appeared as Sir Robert Muir in the Doctor Who story Black Orchid; and has a small role in Yes Minister. He also appeared in the 1974 version of The Pallisers as Barrington Erle and in the Albert Campion mystery The Death of a Late Pig as the Chief Constable. He also played a Chief constable in the 1977 BBC series Murder Most English and Mr Bennet in the 1980 BBC series Pride and Prejudice.