Purves was born in New Longton, Lancashire. He was educated at the independent Arnold School in Blackpool and in the sixth form at Barrow-in-Furness Grammar School for Boys, where he took A-levels. He originally planned to go into teaching, training at Alsager College of Education, but began to act with the Barrow-in-Furness Repertory Company instead.

In 1961, after only one year as a teacher, he turned to acting, initially with the Barrow-in-Furness Repertory Company and later with the Wimbledon Theatre Company. At 26, Purves first appeared in Doctor Who in the role of Morton Dill, an American tourist in The Chase, and then became well known as space pilot Steven Taylor, one of the early time-travelling companions when the Doctor was played by William Hartnell.

After leaving Doctor Who, Purves became a regular presenter on Blue Peter from 1967 to 1978 on BBC One. He co-presented first with John Noakes and Valerie Singleton — the “Val, John and Pete” line-up — and then with Noakes and Lesley Judd. After leaving, he went on to present Kick Start, BBC darts coverage, and became closely associated with Crufts for 40 years.

Now cancer-free and living in rural Suffolk, Peter shows no sign of stopping. He now lives in the Suffolk village of Sibton with his wife, the West End actress Kathryn Evans. In 2024 he appeared as Charles Dickens in a live radio play of A Christmas Carol at the Hawth Theatre in Crawley, and performed the same role in 2025.