Other replies mention Scotland and the SNP, and lest we forget, Scotland is more pro-EU than England, and the last Scottish independence referendum was won on a promise of "stay in the UK and stay in the EU" - yes, really, the threat that an independent Scotland would not be an EU member on day one. (1)
But it's not just about Scotland. Do not forget the question of Northern Ireland, which is now increasingly aligned with the Republic of Ireland. When UK and ROI were both in the EU it was less of a hard choice, but that has changed.
Brexit, while also honouring the integrity of the UK and also the Good Friday agreement is basically about squaring the circle - something has to give. Right now NI is aligned with the Republic of Ireland, not with England, and the Brexiters are not happy about it because NI gets a better Brexit deal by having less Brexit, which doesn't make them look good. But they need to face up to the fact that due to brexit, there has to be a border somewhere between Dublin and London and every position has serious drawbacks. (2)
if NI gets to like the current dispensation well then they might feel like re-joining the republic.
Two fault-lines, not one. It means that the UK needs not one but two wins on throws of the dice in order to remain intact. And a break at one fault-line would trigger restlessness at the other. So the odds of the UK remaining intact go down.
1) https://en.wikipedia.org/wiki/2014_Scottish_independence_ref...
2) https://ukandeu.ac.uk/irish-border-four-acts/