Scotland was only the latest kingdom to join the United Kingdom. Prior kingdoms subsumed within the United Kingdom were: East Anglia, Essex, Kent, Mercia, Northumbria, Sussex and Wessex
They formed the Kingdom Of England and have done so since the 10th century. The Principality of Wales was incorporated into the Kingdom of England in 1536. It wasn't a kingdom and it wasn't united.
The term United Kingdom was not used until after the Union Act of 1707. The Kingdom of Scotland was not subsumed. It joined, in an act of Union not absorption, with the Kingdom Of England to form the hitherto unknown Kingdom of Great Britain. The UK did not exist before 1707.
The last kingdom to join the UK was the Kingdom of Ireland in 1801. We then had the United Kingdom of Great Britain and Ireland, 3 Kingdoms united politically.
When Ireland was partitioned in 1922 Northern Ireland elected to remain as part of the UK. There was never a Kingdom of Northern Ireland, so when Eire was declared a republic in 1949, the Kingdom of Ireland ceased to exist.
So what we have is:-
There are only 2 Kingdoms in the UK, Scotland and England. If they were no longer united then there is in fact no longer a United Kingdom.
There would be 2 nations, the Kingdom of Scotland and the Kingdom of England (which includes Wales) and Northern Ireland.