He was born in county Durham, of Protestant parents who disowned him when he became a Catholic convert. He took his course of humanities at the College of St. Omer, was sent to Liège for his theology, and entered the Society of Jesus at Watten on 28 September 1660. Having completed his studies, he was ordained priest, and spent several years, from 1662, as procurator or agent at the College of St. Omer. He was made a professed father in 1676, and was sent to England the same year.
He resided in London as procurator of St. Omer's College, and was also one of the missionary fathers there. In 1678 labours he was summoned, on the information of Titus Oates, to appear before the privy council, and committed to Newgate Prison. He was tried for high treason with William Ireland, but as the evidence was insufficient, he was remanded back to prison. He was arraigned a second time at the Old Bailey on 13 June 1679, before all the judges of England, together with four other Jesuit fathers. Oates and Stephen Dugdale were witnesses against them, and in accordance with the direction of Lord Chief Justice William Scroggs the jury found the prisoners guilty. They suffered death at Tyburn on 20 June 1679. Fenwick's remains were buried in the churchyard of St. Giles-in-the-Fields.
An account of the trial and condemnation of the five Jesuits for High Treason, in conspiring the Death of the King, the Subversion of the Government and Protestant Religion was published by authority at London, 1679.