That depends on how much potential cash is tied up in the issue. If enough money is involved, they’ll find a ‘moral’ reason stop the UK, with force if necessary.
One of the reasons for the Civil War here was the South’s plan for a 10% tariff, combined with its control of the mouth of the Mississippi. The Yankees saw visions of empty ports and grass growing in the streets of New York and Boston - there was no choice but to go to war...
Good luck with that .... David Cameron has several boatloads of Trident D-5's at his disposal, all MIRV'ed.
Of interest is the mushy language .... it appears that a bloc of EU countries could drag their feet on a secession proposal, and in effect "forbid" that member State to withdraw from the EU.
That would be a sticky wicket.