Wrighte was the grandson of Sir Nathan Wrighte (recorder of Leicester 1680-5 and 1688-96), keeper of the great seal 1700-5, who played an active part on the Tory side in the county election of 1715 (see under Leicestershire). His uncle, William, was recorder of Leicester 1729-62. Returned for Leicester as a Tory on the corporation interest in 1727, he voted against the Administration, except on the motion for the dismissal of Walpole in February 1741, when he was one of the Tories who withdrew. In his only recorded speech, made on 5 May 1738 in a debate on the Spanish depredations in America, he exonerated the Spanish government from responsibility, deprecating measures likely to provoke Spain into war.
He died 27 Jan. 1766.