A large majority of Leave voters think the breakup of the United Kingdom is a price worth paying for Brexit, according to a Sky News poll.
Leave voters were asked if they thought Scotland becoming independent would be a price worth paying for delivering Brexit - 41% said yes, while only 18% said no.
Of the remainder, 17% said they would be happy for Scotland to leave the union regardless of the circumstances and 24% said they didn't know.
The YouGov survey, conducted across Britain, also asked both Leave and Remain voters if they thought Brexit made Scottish independence more likely - 40% said yes.
The opinion poll was undertaken as Sky News travelled to the four constituent parts of the United Kingdom to gauge its fragility.
In our opinion poll, Leave voters were also asked if Welsh independence would be a price worth paying for delivering Brexit. While 28% said yes, 26% said no.
British Leave voters were also asked if Northern Ireland joining the Republic of Ireland would be a price worth paying for Brexit. While 25% said yes, 19% said no.
Professor Sir Tom Devine, of the University of Edinburgh, said that, in the debate on Scotland's future and the future of the United Kingdom, the English nationalist voice would be most powerful.
"It's always been my view that if the union comes to an end, it will come to an end because of either English indifference or hostility," he said. "I think at the moment there's probably more indifference than hostility, but there's little doubt that that is a brand of English nationalism, which is broad. Which in a sense is not really interested on whether Scotland continues in the union or not."
England was the powerhouse behind the Brexit vote and is pivotal in preserving the UK. If the kingdom's biggest and most powerful partner decided it didn't have a future, then it wouldn't have one.
Is there an increase in English nationalism? And with it, a hardening sense that the English regard see an increasing irrelevance in remaining inside the United Kingdom?
John Denham, an ex-Labour cabinet minister and professor of English identity and politics at Southampton University, said: "I think the truth is that there is a set of voters who want England's interests protected, and if for them that means leaving the EU then if that had to be the end of the union they would go along with that, that doesn't mean they're against the union or they want it to break up but if that's what it came down to that's what they would prioritise."
In Northern Ireland, the view of the UK's future tends to split along community lines - this is still a part of the world where politics turns on religious differences.
We went to a hurling double-header semi-final in Armagh. Hurling is Ireland's national game and attracts an overwhelmingly nationalist crowd.
Brian MacAvoy, chief executive of the Ulster Gaelic Athletic Association, can see a united Ireland through the Brexit fog: "I think Brexit has put the future of the United Kingdom at its greatest ever risk.
"I think the whole idea of a new Ireland, a united Ireland is more so now to the forefront of the agenda than ever it was before, a referendum in Scotland is back on the cardsâ€¦. I do think the long term future of the United Kingdom, Brexit is the one thing that has put that most in danger than ever before."
Boris Johnson has caused deep anger among unionists with his Brexit deal. The proposal for a customs border down the Irish Sea has raised the spectre of instability.
We visited the East Belfast Constitutional Club, where the talk is of what they see as Brexit betrayal and, ominously, protest.
Moore Holmes, a unionist activist, told us: "As soon as you allow the threat of violent republicanism to achieve political gain you do run this risk of tensions being heightened, extreme sensitivities, and these public protests in rejection can lead to other things and I would first and foremost condemn that, I wouldn't want to see that, we don't want to see that happen but there is a risk."
Dr Katy Hayward, of Queen's University in Belfast, told us: "Unsurprisingly, Brexit is having very differing effects on people's views of Irish unity so those who are in favour of Irish unity are increasingly likely to think it's going to happen and that they want it to happen.
"Those who are opposed to Irish unity or are wary of it are increasingly resistant to it and it's that polarisation and the sort of reinforcement of difference that we are beginning to see through Brexit that would be quite worrying I think for the longer term peace process."
In Wales, we dropped in on the Caernarfon Male Voice Choir. They have recently celebrated their 50th anniversary. If the faces have changed over the years, so has the political outlook. I asked choir member Gruffydd Penrhyn Jones if Brexit has diminished his sense of Britishness. He replied: "I think it has, it has split us up."
"If Scotland leaves the UK I would feel like a little brother who sees his big brother leave the patriarchal home and make his own way in the world, I would be glad for him but sad for me."