However your point on the leave campaign is only one side of the story; The BBC's coverage of the lead up to the referendum was overwhelmingly pro-remain, the figures I've seen (though I don't have them to hand) were 80% pro-remain coverage.
Additionally, the remain campaign had full overt government backing; Every single household in England recieved a flyer explaining why David Cameron and his cronies thought that the UK should remain, which is much more penetration than any slogan on a bus could get.
Thanks for your reply, it's nice to have a reasonable debate with people with differing opinions on this matter, usually I just get called racist for voting leave and have trouble explaining my views after that.