The main reason they left the EU was xenophobia. Someone said earlier in this topic that Brexit is like a kid running away from home without any idea what to do next.
More a combination of xenophobia and a psychological desire to have more power. The irony is that under this Tory government, employment has steadily increased meaning job competition has increased (causing the greater difficulty for people to gain jobs), public services etc. have been massively cut and inequality among age groups, genders, races and class groups has rapidly increased. But somehow, the Tory lead campaigners of the Leave Campaign managed to manipulate all of that and blame it entirely on immigrants, and the majority of Britons fell for it.
A few days later, those same campaigners admitted they had no plan. As many people pointed out, including the French Foreign Minister, these campaigners lied and manipulated hundreds of thousands of people. Some of these people have realised they were conned and aren't as xenophobic as they were before, but the majority of them still can't see the obvious truth.
Britain is in a sad state of affairs right now. With great economic and security uncertainty across the world, the threat of extreme international terrorism and revolts breaking out across the globe, Britain faces an identity crisis. The people of Britain have lost trust in 'the establishment' because of the failure that was the Iraq War, the failure to address those responsible for the Global Banking Crisis of 2009 and several other factors. Now Britons are searching for their new identity and developing overly nationalist pride. Inevitably it'll come back to bite us.
I honestly hope we don't have anymore elections or referendums for the foreseeable future, primarily because the majority of Britons will be suckered in by the same repeated lies of the Conservatives and vote blindly for the same politics as usual whilst moaning about how hard life is.
