…but PM Theresa May put Brexit up for vote in Parliament it and was ultimately ruled out?
Jason Weaving

Complicated, indeed.

A vote has not been held in Parliament for Brexit. A public referendum on Brexit was conducted earlier this year. The High Court just ruled last week that Parliament ‘should have the final say’ on Brexit. PM May is still trying to subvert the Parliamentary process by appealing to the Supreme Court to allow her government to invoke Article 50 (exiting the EU) without Parliament.

Apologies, but I must disagree on your assertion of false equivalency. Donald Trump share many things with Brexit. There has been much research on both the candidate/movement and the British Referendum and it is clear they are similar. In summary, they share a core demographic, the supporters share a core ideology (authoritarianism), and the shared overarching theme of each is anti-establishment.