Following employment in mining as a Bevin Boy in World War II,[3] he developed his performing skills further during his national service with the British Army's Combined Services Entertainment unit, working alongside comedy actor Kenneth Williams, actor Peter Vaughan, film director John Schlesinger and dramatist Peter Nichols, who used the experience as the basis for his play Privates on Parade.
In 1969, Baxter performed in the original production of Joe Orton's then controversial farce What the Butler Saw at the Queen's Theatre in the West End with Sir Ralph Richardson, Coral Browne and Hayward Morse.
Baxter remained a great favourite on the Scottish pantomime circuit, especially at the King's Theatre, Glasgow, up until his retirement in 1992.
[6] In 1994, he returned to radio, taking the role of Noël Coward in the BBC World Service Play of the Week, Marvellous Party[7] directed by Neil Cargill.
Also with Cargill, he read Whisky Galore[8] and Jimmy Swan – The Joy Traveller[9] for BBC Radio, providing the voices of all the characters.
Baxter guest-starred in an episode of The Goodies and later appeared in the lead role in Mr Majeika, developed from the books by Humphrey Carpenter, a children's show about a magic teacher, expelled from Walpurgis (the wizard land) for failing his professional examinations.
He later stated that he had wanted to retire after his spectacular hour-long shows had been cancelled and that the move to children's television was a "purely financial" arrangement.
[12] Baxter appeared in a number of films, including Geordie (1955), Very Important Person (1961), The Fast Lady (1962), Crooks Anonymous (1962) and Father Came Too!
[15] In August 2014, Baxter was one of 200 public figures who were signatories to a letter to The Guardian expressing their hope that Scotland would vote to remain part of the United Kingdom in September's referendum on that issue.
Five years before then, Baxter had been arrested for cottaging and contemplated suicide for fear of scandal causing an end to his career.