He was born in Much Hadham, Hertfordshire, the son of Thomas Randolph, President of Corpus Christi College, Oxford and educated at Westminster School and Christ Church, Oxford.

He retained the post of Regius professor until his move to Bangor.

In debating the expansion of free schools, he noted that educating the poor would "...puff up their tender minds or entice them into a way of life of no benefit to the publick and ensnaring to themselves.

"[citation needed] On 12 June 1809, he was made the Bishop of London, and ex officio a member of the Privy Council of the United Kingdom.

He had married Jane, daughter of Thomas Lambard of Sevenoaks, Kent in 1785; they had six children.