I've heard it said by London types that when the referendum results was announced they were so shocked because they had never met a person who wanted to vote leave and thought they only existed on TV, Farage and the like.
My own personal experience is that I know a few people who voted remain, a few who voted leave, some were very passionate on each side, some were much less fussed like myself. The majority of people I know/met though, didn't seem to care either way and didn't bother voting, and still today they don't really care either way.