Unfortunately, many people knew they were being lied to about Brexit but liked the lies they were being told so voted for it anyway. Ditto Trump in the US. Lies that enable people to think they have control (vote Brexit and the NHS will get £350 million a week extra for the NHS.....the power is in your hands) or lies that make people think they have been hard done to (Dems stole 2.5million votes) are one that people can buy in to. Keeping Muslims out of the country was another notion that went down well with enough people to help swing the Brexit vote. The "taking back control" of borders being thinly veiled (hurrah) racism. This notion sat particularly well with the white, male, northern, obese and less well educated. Prof Danny Dorling's research into Brexit voting patterns is a real eye opener. The ultimate irony is that the government now has cabinet members who are the offspring of immigrants try to enforce our borders to keep the immigrants out and stop them taking our jobs!