> See the last 15 years of UK voters being worried about immigration levels, vs immigration levels.

Look, let's be clear here. The UK (as a member state) was concerned that the EU was becoming too federal. Therefore (following Machievelli) they decided to push for new members, mostly the eastern bloc countries.

Then, politically, it was difficult for them to refuse to allow immigration from those countries (many of the other members had a moratorium for a few years post-accession). This lead to lots of British people becoming very upset, at the EU for some reason (even though their government had done this).