Left early an orphan, Wright was brought up in his mother's family, who sent him to boarding schools at Attercliffe, near Sheffield, and Darton, near Wakefield.

For a short time he was chaplain to 'the Lady Susannah Lort' at Turnham Green, preaching also the Sunday evening lecture at Dyott Street.

In 1705 he was chosen assistant to Benjamin Grosvenor at Crosby Square, and undertook in addition (1706) a Sunday evening lecture at St. Thomas's Chapel, Southwark, with Harman Hood.

On the death (25 January 1708) of Matthew Sylvester, he accepted the charge of 'a handful of people' at Meeting House Court, Knightrider Street, and was ordained on 15 April; his "confession of faith" was appended to The Ministerial Office (1708), by Daniel Williams.

Among Protestant dissenters he ranked as a presbyterian; his will explains his separation from "the common parochial worship" as an act of service to "catholic christianity".

Hughes gives a list (revised by Wilson) of forty-three publications by Wright (nearly all sermons), adding that he published several anonymous pieces.

After long illness, he became a nonconformist through the influence of William Cotton, a wealthy ironmaster of Wortley, near Sheffield, whose daughter Elinor (d. 1695) he married.

He died on 3 April 1746, and was buried in the south aisle of Stoke Newington church, where is a Latin inscription (by Hughes) to his memory.