Quotes from the news wire:
English voters, especially, leave voters, tend to prioritize their English identity and want English interests put ahead of the Union, it's not that they are anti-union, it's that their idea of Britishness is as an extension of Englishness and English interests. If the two come into conflict then they prioritize English interests.
The English-centric idea of union was fostered as part of the imperial Great Britain and Northern Ireland, the truth is that old idea of the union lost its sense of purpose decades ago. And in that time, the other parts of the union asserted their identity( or in Northern Ireland, identities). If government really wants the union to survive, it has to be a partnership between all the nations.