His inaugural dissertation, De distinctis et con-fluentibus Variolis (Leyden, 1724) was included by Albrecht von Haller in the fifth volume of his Disputationes ad Morborum Historiam et Curationem Facientes.
Clifton afterwards settled in London, where his classical and scientific attainments won him the friendship of many eminent men, including Sir Hans Sloane, at whose instance he was elected a fellow of the Royal Society on 22 June 1727.
The same year he published Hippocratis Coi Operum quse extant omnium secundum Leges artis Medicae dispositorum, editionis novse specimen, (London, 1727), which was followed in 1732 by Proposals for Printing, by subscription, all the works of Hippocrates in Greek and Latin, digested in a new and regular manner, but from want of encouragement the intended publication never appeared.
Writing to Sir Hans Sloane from Kingston in that island on 3 June 1736, he says : "My misfortunes came so fast upon me, and my brother's provocations were so frequently repeated, that I was hurried in a manner to death about 'em".
granted on 6 Nov. 1736 to his widow, Clifton is described as "late of the parish of St. George, Hanover Square, Middlesex, but at Kingston in Jamaica, deceased".