But the UK appears to have no control over foreigners wherever they are resident.Most countries have a requirement in law that property.. or real estate, what the continentals call" immobiles ", can only be purchased by citizens. With property comes the duty to pay taxes and the right to elect political representation. So generally a non citizen needs to have a legal contract with a citizen who owns the property as a proxy. What the EU did was to assign a right to any citizen of the 28 member countries to own property in any of the 28 countries.
Within the EU you can, as usual, argue a level of fairness based on the idea we have the same rights in the EU27 as they have here.