Why did Brits vote for those who want more migrants?
First of all, because they have a two-party system like the US, voters can only choose between one and the other.
Secondly, because all parties promised to address illegal immigration and immigration as a whole. The grave mistake of the constituency was not asking for details.
The current government in the UK is dealing with migrants and illegal immigration in its own way. They want to get rid of the native British population and import their replacement, so ultimately, there won't be immigrants or illegal migrants. If all residents of the country consist solely of immigrants, legal or not, such a distinction becomes meaningless. It is a brilliant idea, isn't it?