"The EU is not as popular in many countries now, due mainly to the free movement of people, especially from Eastern Europe."
Yes, I believe those poor countries (mainly from Eastern Europe) who receive most EU funding are happiest with the EU. The ones contributing the most are not so enamoured. Strange that. 
Son was working in France recently and said anti-EU feeling just outside Paris was very strong. In one town the EU flag was being replaced in the town centre as locals had ripped it down. When workmen came to replace it they were booed.
Where is the love for the EU? I think our own Remainers are its biggest fans.