He was the sixth son of Peter Newcome, vicar of Aldenham, Hertfordshire.
He was admitted to Queens' College, Cambridge in 1718, matriculating in 1719, and graduating B.A.
He was rector of St Botolph's Church, Cambridge, in 1727.
From 1746 he was rector of Whitchurch, Shropshire, and from 1755 canon of Windsor.
He was bishop of Llandaff from 1755 and was translated to St Asaph in 1761.