Except it's not united. You see, in 1707 when the union was created, it was England + Scotland = Great Britain. Then in 1800, Great Britain plus Ireland = United Kingdom. Ireland got independence in 1922 (Northern Ireland declared independence from Ireland one day later and rejoined the UK, much like Crimea rejoining Russia from the Ukraine recently, except that that one took 25 years). With Scotland gone too, only one of the entities that originally formed the United Kingdom remains. England. Wales and Northern Ireland aren't kingdoms, hence, no more United Kingdom without Scotland.
That's also my understanding, JAS84.
Technically the United Kingdom ceased to exist in 1922, as only one Kingdom remained - that of Great Britain: the same as after the 1707 Acts of Union. As you correctly stated, neither Wales nor Northern Ireland are kingdoms. However, that was conveniently ignored at the time, and can be again.
Separating the Kingdom of Great Britain back into its pre-1707 parts doesn't really change that fact as there will still only be one kingdom in the nation state - but it gives the opportunity to include Wales in the name of the country.
However, just the
Kingdom of England, Wales and Northern Ireland
would be more (if not totally) accurate.
Former United Kingdom (using the precedent of the
Former Yugoslav Republic of Macedonia
) was suggested by Newsnight, in jest, as you have to consider the abbreviation would be most unwelcome.