Green’s Dictionary of Slang

(Aus. / US) a Briton.

1905		Sun. Times (Perth) 3 Sept. 1/5: One or two of the bli’me push rend the air with choice Billingsgate.
1918		Literary Digest 6 July 62: I overheard two ‘blimeys’ [...] while they hunted a shell-hole.
1939		Howsley Argot: Dict. of Und. Sl. 8: blimey – an English cockney.