He later appeared in a series of three half-hour radio sitcoms for BBC Radio 4, and also recorded a number of plays for the station.
Baxter also appeared in a number of films in the 1950s and 60s, and received a lifetime achievement award at the British Comedy Awards.
Bafta Scotland gave Baxter its Outstanding Contribution to Film and Television Award in December 2020.
Baxter always considered himself a character actor rather than a comedian and was a reluctant celebrity, giving few interviews and declining to appear on chat shows.
At the age of 94, he confirmed he had always been gay but said he had initially hidden the truth to avoid arrest in the years before decriminalisation.