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.
From my point of view they helped create the problem by running Farage et al on Question Time far more often than the electoral popularity of their party would warrant.
The leave campaign was extremely successful because it targeted different groups of interests with different messages. That's why none of those different interests can now agree on the final outcome.
If I was you I'd also be slightly dubious about the dark money behind all of the pro Brexit 'grassroots' campaign groups.