Given the hypothetical question: "Given the choice between leaving the EU and breaking up Britain, which is more important."
I would not be able to give a 100% answer without numerous caveats.

Leaving the EU is very important, and if we don't do it now, the only opportunity we've had since 1973, it may be a very long time before we get the opportunity again.
Keeping the UK together is also very important, if it wants to be kept together. Even without Brexit the Scots have had a referendum on separation, and the rest of the UK had no say in that referendum. That could happen again. It would be a shame if Brexit failed just because we wanted to retain Scotland, and the Scotland decided to leave at a later date.

Similarly with Northern Ireland. I would want to keep them as part of the UK, if that is also the wish of the majority of those who live there. If Jim Carroll is right in his claim that the majority of those in the North now favour a united Ireland it would again be a shame to lose Brexit when we may lose Northern Ireland anyway.

I don't honestly believe that Brexit will force a break up of the UK, although it may facilitate it if parts are already wishing to leave.
So, as it seems to be a one-off opportunity, my feeling would be for continuing with Brexit.

As the Spectator article says it is a hypothetical question. Being in favour of Brexit doesn't mean being in favour of the break-up of UK.

Would anyone else care to respond with their honest view of the question?