Purves had originally planned to go into teaching, but instead began acting with the Barrow-in-Furness Repertory Company. He first became well-known to television audiences in the mid-1960s as Steven Taylor in Doctor Who. He has made cameo appearances as himself in episodes of programmes such as the soap opera EastEnders and the hugely popular sitcom The Office. Purves is depicted in the 2013 docudrama An Adventure in Space and Time by an uncredited actor in one scene recreating the press photocall announcing Jackie Lane's casting in the series.