Terebus, "The country which has contained all three has existed since 1801 and it was called the United Kingdom, it will remain being known as such."

You should have said "The PART of the country ....."
When the existing UK and NI breaks up, both parts will have all the memberships you mention or they will have none. Are you seriously saying that all the benefits given to the UK by the EU will continue when the land mass and population will be diminished?

Two new states as McGrath of Harlow very clearly, concisely and logically spells out.