The free movement of persons, including visa-free travel within the European Communities, was established by 1964, long before the UK joined the European Communities.
The UK has never joined the Schengen Agreement providing for passport-free travel between its signatories.
The UK retains full control over its borders, including in respect of EU citizens and UK nationals.
The UK can restrict entry to its territory on grounds of public health and public security, subject to the principle of proportionality.
The Settlement Agreement contains agreed restrictions on the rights of non-UK EU nationals to claim in work benefits within the UK for a period of up to 9 years.
A broader restriction on the rights of EU nationals to enter the UK would be a significant derogation from principles of the EU Treaties that were in place long before the UK joined the European Communities.
For so long as it remains a member of the EU, the UK has a veto over new members of the EU and the terms on which such members are permitted to join.