Blomefield was educated at the grammar schools at Diss and Thetford in Norfolk. In April 1724 he was admitted to Caius College, Cambridge, where he graduated with a Bachelor of Arts degree in 1727 and a Master of Arts degree in 1728. He was ordained a priest on 27 July 1729 by Thomas Tanner, then Chancellor of the Diocese of Norwich, later Bishop of St Asaph. Two days later, on 29 July 1729 he was appointed Rector of Hargham in Norfolk, by the patron Thomas Hare, and shortly afterwards on 13 September 1729 was appointed by his father, whose turn it was at that time as patron, as Rector of Fersfield.
