Brandon was the son of Charles Brandon, a doctor of Maidenhead, was apparently born at Bray, near that town, about 1644.
He entered Oriel College, Oxford, as a commoner on 15 February 1661–2, and proceeded B.A. on 11 November 1665. Anthony Wood says that "he entertained for some time certain heterodox opinions, but afterwards being orthodox", took holy orders. He became rector of Finchampstead, and for some years preached a weekly lecture on Tuesdays at Reading.