I've sometimes put the term 'pre-Socratics' in scare quotes when using it (thus: "'pre-Socratics'", for you use-mention fans). Kurt Pritzl in his first lecture of the 'pre-Socratics' lecture series speculated that Diels-Kranz, Die Fragmente der Vorsokratiker, was responsible for the term's influence and was perhaps even (derivatively in English) its origin. Someone else in a discussion on James Warren's Kenodoxia (here and here) has pointed to Grote's usage.
According to the OED, the provenance of the term is indeed German, but its first occurrence in English is from 1838, and Burnet was already using the term with scare quotes!
You may see for yourself what is apparently the first usage, in Morrison's translation of Ritter, here (courtesy, Google books).
1838A. J. W. MORRISON tr. A. H. Ritter Hist. Anc. Philos. I. 179 (heading) History of the Pre-Socratic philosophy. 1856J. H. SEELYE tr. A. Schwegler Hist. Philos. in Epitome III. i. 17 The universal tendency of the pre-Socratic philosophy is to find some principle for the explanation of nature. 1892J. BURNET Early Greek Philos. 2 The common practice of treating this younger contemporary of Sokrates [sc. Demokritos] along with the ‘pre-Socratic philosophers’ has obscured the true course of historical development. 1957G. S. KIRK & J. E. RAVEN Presocratic Philosophers p. vii, We have limited our scope to the chief Presocratic ‘physicists’ and their forerunners, whose main preoccupation was with the nature (physis) and coherence of things as a whole. 1974Nature 8 Nov. 130/2 In the treatment of Greek science emphasis is laid upon the importance of the presocratic belief that causal relationships existed between natural phenomena. 2001Brit. Jrnl. Hist. Sci. 34 380, An awareness of what might be called ontological objectivity..was implicit in the speculations and enquiries of some of the pre-Socratic thinkers, Plato and Aristotle. 1876S. F. ALLEYNE et al. tr. E. Zeller Plato & Older Acad. p. viii, Character in relation to Socrates..To the pre-Socratics. 1889Mind 14 603 It was transformed into a monism like that of the pre-Socratics. 1945B. RUSSELL Hist. Western Philos. (1946) I. xiii. 126 ‘The Good’ dominated his [sc. Plato's] thought more than that of the pre-Socratics. 1972E. HUSSEY Presocratics i. 1 What gives the group of Presocratics such unity as it possesses is..that all these men were involved in the movement of thought which led to the separation of science and philosophy from one another and from other ways of thinking. 1994H. BLOOM Western Canon III. x. 261 While the pre-Socratics and Freud agree that there are no accidents, Austen thinks differently.