Born John Nicholson, he was educated at the Royal High School in Edinburgh, where he was active in the dramatic society.
McGlynn's roles include that of vet Calum Buchanan in the British television series All Creatures Great and Small between January 1988 and September 1989.
McGlynn's debut as a professional actor was in 1975 at the Young Lyceum Theatre in Edinburgh, Scotland, in a new play, If Ye Died wi' a Face Like That, by Glaswegian writer William Grant.
He remained with the company for the next two years, performing as an actor, drummer and singer in Cry Wolf, The Water Babies, A Midsummer Night's Dream and Under Milk Wood.
After 7:84 ceased operations, McGlynn was engaged by the Wildcat Stage Productions, which emerged from it, in His Master's Voice and The Complete History of Rock'n'Roll.