Perhaps ultimately not a reality, but the likely scenario 'if' such a thing were to happen, would be more likely a secession from the UK by Scotland and/or Northern Ireland, that could potentially draw in the Republic of Ireland.Although it is a very emotive issue in England, it's not really emotive enough to mobilise people to fight for it either way. There's more chance of a civil war if X Factor was to be cancelled.
Oh yeah, I don't think there would really be any fighting. Just tossing out the idea of a modern civil war biased off other imagineary Civil Wars. Free state of liverpool, modern borderers digging in along the Scottish front sort of thing. More so an excuse for folks who already have tons of modern UK troops to fight the troops against each other. I am sure things will settle and come to a since of normalcy once all the chicken littles stop running around crying that the sky is falling.