Radcliffe was born in Wakefield, Yorkshire, and graduated from Oxford University to become a Fellow of Lincoln College. He obtained his M.D. in 1682 and moved to London shortly afterwards. There he enjoyed great popularity and became royal physician to William and Mary. In 1713, he was elected to parliament as member for Buckingham. On his death in the following year, his property was bequeathed to various charitable causes, including St Bartholomew's Hospital and University College, Oxford.