A good guide to the outcome is found in the odds quoted by the bookies. Bookies are not in business to spread propaganda, their objective is to make money.
The current odds at Betfair are:
8/15 means that you bet £15 to win £8. £15/8 means you bet £8 to win £15. So the people betting with Betfair think the result is more likely to be remain than leave.
Ladbrokes offer 8/15 for remain, 6/4 for leave.
William Hill offer 1/2 for remain, 13/8 for leave
Coral offer 8/15 for remain, 11/8 for leave
So as you'd expect, the odds offered by all these bookies are much of a muchness. The betting public tend to think that the UK will remain.