Brexit wasn't a party issue, it was a referendum, so citing it as an example of two-party politics is a bit odd. Other European countries have also had referendums on aspects of the EU that were extremely bitter, often because the pro-EU side lost and then simply ignored the results/asked again.

It wasn't a near-perfect 50/50 split either. It was 52/48, which yielded a large margin of ~1.8M more votes to leave. Referendums in societies that only have them rarely will always be somewhere around the middle point, of course, as if there was already a clear majority in favour of one direction then it'd have been implemented already without the need for a referendum.