Born at Sibsey, Lincolnshire, on 6 April 1772, Marrat was self-taught through wide reading and study of modern language.
In 1811–12 he, in conjunction with Pishey Thompson, ran The Enquirer, or Literary, Mathematical, and Philosophical Repository, Boston.
[2] From 1833 to 1836 Marrat was mathematical tutor in a school at Exeter, but on the death of his wife he returned to Liverpool.
During 1814–16 he wrote The History of Lincolnshire, which came out in parts, and after three volumes had been published, it was stopped: Marrat alleged this was a consequence of Sir Joseph Banks's refusal to allow access to his papers.
[1] An anonymous Geometrical System of Conic Sections, Cambridge, 1822, was ascribed to Marrat in the catalogue of the Liverpool Free Library.