At age 12 he was sent to Westminster School, and in 1732 he was elected from the foundation to a scholarship at Trinity College, Cambridge, but entered Christ Church, Oxford as a commoner.
At All Souls he formed lasting friendships with Sir William Blackstone and Dr. Benjamin Buckler, whom he assisted in drawing up the Stemmata Chicheliana.
[1] In 1746, during the Jacobite rebellion, Bingham served the office of proctor in the university, and acted with great spirit.
His eldest son, the senior scholar at Winchester, was accidentally drowned while bathing in the river Itchin in 1708.
In 1781 Bishop Bagot offered him the Warburtonian lecture, but he declined to preach it, because he held that the church of Rome, though corrupt, was not chargeable, as Warburton meant to prove, with apostasy.