Good comments above and, Slobodan, quite right - there should have been a stronger requirement for entry into such formal arrangements in the first instance. Unfortunately, the UK, specifically, has almost no previous history of referenda and chose not to look at its former colonies for guidance. Australia, Canada, and the US, for example, all require super majorities and also make use of regional majority requirements (i.e. states or provinces). Simple, first past the post, with voluntary voting, is always open to a significant minority decision. Super majorities pretty much remove any room for complaint, even if the absolute numbers are still short (for example, in the Brexit, 67% of 72% would have been 48% of eligible voters but still far less controversial or arguable than what resulted).
Voluntary versus mandatory voting is another discussion (and typically everyone argues in favour of the arrangements under which they live :-) ).