In 1960, Vernon appeared in an adaptation of A.J. Cronin's novel, The Citadel. In 1961, he played the father in the BBC series, Stranger on the Shore, famous for Acker Bilk's hit theme song. An early leading role was as wartime agent-turned-criminologist Edwin Oldenshaw in the TV series The Man in Room 17 (1965–66) and its sequel The Fellows (1967). He also played a small role as Colonel Smithers, an executive of the Bank of England, in a scene opposite Sean Connery and Bernard Lee in the 1964 James Bond film Goldfinger, discussing how Auric Goldfinger transports his gold overseas.
He is remembered for his parts as the unnamed 'city gent' reluctantly sharing a train compartment with the Beatles in A Hard Day's Night, the planetary designer Slartibartfast (designer of fjords) in the BBC radio and TV series The Hitchhiker's Guide to the Galaxy, as Sir James Greenley ("C") in The Sandbaggers, as Lord Salisbury in Edward the Seventh, as Major Toby Smith-Barton in The Duchess of Duke Street, as the Duke of Broughton in Nanny, as the occasional character Sir Desmond Glazebrook in the TV series Yes Minister and Yes, Prime Minister, and as Mr Becket in Sammy's Super T-Shirt. He also appeared in the 1965 Morecambe and Wise film The Intelligence Men as patron of the arts Sir Edward Seabrook, Lord Bartelsham in Ripping Yarns, and Squire Dale in the BBC Radio 4 adaptation of The Small House at Allington. He played Admiral Croft in the 1971 BBC television adaptation of Persuasion. In 1986 he appeared in Paradise Postponed, and voiced the professor Gus in The Giddy Game Show (1985-7). He also appeared in the final episode of the BBC's television production of Rumpole of the Bailey (1992) as Rumpole's exculpatory dentist, Lionel Leering, and in the last series of Lovejoy (1994) playing Tinker's brother-in-law.
On radio, in 1978 he played Sir Gerald Tarrant in a BBC World Service adaptation of the Modesty Blaise book Last Day in Limbo and Professor Misty in the BBC Radio 3 sitcom Patterson in 1981. He also starred in the title role of Lord Emsworth in several BBC Radio 4 series of Blandings between 1985 and 1992.
His final film appearance was a cameo at the end of the family film Loch Ness, which was released in 1996.
He died of complications from Parkinson's disease on 4 December 1997.
