The son of John Berriman, apothecary in Bishopsgate Street, London, in the parish of St. Ethelburga, by Mary, daughter of William Wagstaffe, of Farnborough, Warwickshire, and grandson of the Rev.
He moved on to Merchant Taylors' School, London, under Matthew Shorting, in 1700.
Berriman was ordained deacon at Oxford by Bishop William Talbot, but continued in residence at the university till he was settled in London on 5 May 1712.
He became domestic chaplain to John Robinson, bishop of London, April 1720, and resided at Fulham.
In 1723–4 was delivered his Historical Account of the Trinitarian Controversy, the Lady Moyer's lecture, published 1725.