Your example demonstrates that the UK meets the definition of a state but not necessarily the definition a nation (shared culture/identity).

The UK is a state, but arguable as a nation from certain points of view. It is not a federal system as some think it is. In fact, even the relatively recent UK supreme court may very well be unconstitutional.

France has been more heavy-handed with uniting its nation, but even it has issues. Spain is possibly looser than the UK, at least outside the sporting arena.