It's true that it was almost a 50:50 vote, Stu. But the enormous rise in anti-foreigner attacks suggests that the vote was won by that tainted dream.

From the New Statesman: As Lord Ashcroft's polls suggest, it is only the white working class (if by this we mean C2/DE, though many in DE are unemployed) who voted for Brexit. In fact, those describing themselves as "in employment" generally voted to Remain. Those describing themselves as Asian, black or Muslims overwhelmingly voted Remain. By contrast, nearly six in ten white Protestants voted to leave.
Brexit was a rejection of British multiculturalism. That is the real take-home message of the Ashcroft polls. Of those who see themselves as "English not British", 80 per cent voted to Leave, irrespective of social class. Those who see themselves as "British not English" voted 60 per cent for Remain. Similar patterns (and similar press involvement) can be found in the Quebec referendum of 1995, which failed by a narrower margin than Brexit succeeded.