In 1786 he was one of seven architects who were consulted on additions to the House of Commons, and he and another carried out the execution of James Gandon's design for the work.

[1] In December 1788, William Burton Conyngham commissioned Murphy to make drawings of Batalha Monastery in central Portugal.

[1] Settling again in England in 1809, Murphy took out a patent in 1813 for a method of preserving timber and other substances from decay.

A large folio volume of his drawings of arabesque ornaments went to the library of the Royal Institute of British Architects.

[1] Murphy was unmarried, and his estate of £5,000 was administered in November 1814 by his sister, Hannah, wife of Bernard McNamara.