In spite of what
Americans may think, the image of
Englishmen - and particularly
Londoners perpetrated by
Dick Van Dyke in
Mary Poppins does not exist (especially not with that godawful
accent). 'Blimey' itself is not particularly common, but it can occasionally be heard.
Confession time: I've got into the habit of using 'blimey' myself. I don't know why.