And yet the country voted for Brexit, mostly without even knowing what they were voting for.

I agree with the OP that politics in the UK are toxic. There are only 2 parties that matter, and they are essentially the same, even though they would have you believe differently. The parties never work together, and spend all their time shamelessly sniping at one another and blocking bills based on political points scoring. It doesn't feel like either party wants what is best for the populace.

Then you have the tabloid media, which constantly fans the flames of hatred and outrage, poisoning the minds of a large part of the populace, essentially able to make them believe almost anything that suits the narrative of the owner's political affiliation.