The UK is not a 'nation state'.
There's more than one definition, I use the one used by Philip Bobbit (roughly) that is about the relationship between the government and the people:
The government provides services for the population to improve their standards of living (infrastructure, education, legal protections etc)
The population supports the government and when the government calls for it - makes sacrifices for the common good (including going to war)
This model came into being with the nation state (and non-ethnic-based nations adopted it because of its utility).
When people talk now about the death of the nation state they're talking about the death of this model (see the English government increasingly withdrawing from providing public services).