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Not sure what that means. What do you think the Uk claims to own?

Lots of european countries owned colonies until the post-war settlement.

And immigration to UK is at an all time high so not sure on other point?

Immigration to the UK is not at an all time high - both immigration and net migration are down pretty sharply:

The general trend of the past years has increased immigration

Its not an open border and the rules changed and now it is decreasing