Gulliver was born at Banbury, Oxfordshire, on 4 June 1804, and after an apprenticeship with local surgeons entered at St. Bartholomew's Hospital, London, where he became prosector to Abernethy and dresser to Lawrence (afterwards Sir William).
Gulliver wrote no systematic work, although he edited an English translation of Gerber's General and Minute Anatomy of Man and the Mammalia in 1842, adding, besides numerous notes, an appendix giving an account of his own researches on the blood, chyle, lymph, &c. In 1846 he edited for the Sydenham Society The Works of William Hewson, F.R.S., with copious notes and a biography of Hewson.
Gulliver was the first to give extensive tables of measurements and full observations on the shape and structure of the red blood-corpuscles in man and many vertebrates, resulting in several interesting discoveries.
In some points he corrected the prevailing views adopted from John Hunter as to the coagulation of the blood, at the same time confirming other views of Hunter; he noted the fibrillar form of clot fibrin, the so-called molecular base of chyle, the prevalence of naked nuclei in chyle and lymph, and the intimate connection of the thymus gland with the lymphatic system.
To pathology he rendered important services, showing the prevalence of cholesterine and fatty degeneration in several organs and morbid products, the significance of the softening of clots of fibrin, and some of the characteristics of tubercle.