Warburton was born on 24 December 1698 at Newark, Nottinghamshire, where his father, George Warburton was town clerk. He was educated at Oakham and Newark grammar schools, and in 1714, he was articled to Mr Kirke, an attorney, at East Markham. In 1719, after serving his articles he returned to Newark, where he began to practise as a solicitor, but, having studied Latin and Greek, changed his mind and was ordained deacon by the Archbishop of York in 1723. He was ordained as a priest in 1726, and in the same year began to associate with literary circles in London.