I agree that the EU would not like it if Piddlington voted to become independent or even a US territory. But what legal issues do you think the EU would be able to raise? Britain is no longer part of the EU.
UK on the other hand...
Sorry! Piddington it should be.
In some ways, that is a distinction without a difference.
England will continue being effected by the EU, since so many of their neighboring countries, such as France, remain a part of the EU. Wherever France exists, their failed border policies will follow.