Not true. British people are the EU’s biggest beneficiaries of the right to settle anywhere in the EU: more British people live in other EU countries than any other nationality! And there are almost as many Brits living elsewhere in the EU as there are other EU nationals in Britain. Evidence
In reality, only 3.6% of the UK population is from another EU country. Most migration in the UK is from outside the EU, which means freedom of movement rules don’t apply and it’s completely up to the British government how to manage this migration. Evidence
And EU migrants are net contributors to the economy. Between 2001 and 2011, they contributed 34% more in taxes than they took out in benefits and services. Evidence
Compared to the UK average, EU migrants are more highly educated, more likely to be employed, and much less likely to claim benefits. Evidence
There’s the further point that being part of the EU helps us to manage migration from outside the EU more effectively. For more details, see my detailed briefing on migration.