Wagstaffe was born in Cublington, Buckinghamshire, UK, The only son of the town's rector, and related to the Wagstaffe family of Knightcote, Warwickshire.

He was educated at a school in Northampton, entered Lincoln College, Oxford in 1701, and graduated B.A.

The same year, he joined the London "practice of physics" of his relative Thomas Wagstaffe.

He became a fellow of the Royal College of Physicians on 22 December 1718, and was a censor in 1720.

This United Kingdom biographical article related to medicine is a stub.