An exclamation of surprise.
A euphemism (specifically a minced oath) derived from 'God blind me'.
Blimy is first recorded in print in Barrère and Leland's A dictionary of slang, jargon and cant, 1889. The extended version was used, by Arthur Morrison in A Child of the Jago, 1896:
"Gawblimy, not what?"
The link between 'gor blimey' or 'cor blimey' and 'god blind me' was made evident by James Joyce in Ulysses, 1922:
God blimey if she aint a clinker
Being as it is, a contraction of 'God blind me', the term was originally spelled 'gorblimey' and is still frequently used that way.