It solves lots of the historical problems with the United Kingdom of Great Britain and Northern Ireland, if only by shortening the ridiculously long name for a country - one of the longest on record and more a short essay than the name of a state. It also solves the problem of lots of people not being particular happy with the present arrangement and having various ambitions to belong or not to belong either to England or to the European Union. Some want in; some want out; some want both at the same time it seems, at whatever level you look at it.
The solution is the Union of Scotland and Ireland (both North and South) and the Kingdom of England and Wales.
Northern Ireland, which has always been a problem, both for Ireland and for England gets the best of both worlds. The Protestants, most of whose ancestors came from Scotland not England and so are mostly Presbyterian rather than Anglican only ever really had a loyalty to England as the dominant partner in the United Kingdom of England and Scotland and because in those days Scotland was more Catholic than Protestant. Now of course, Scotland is firmly Protestant to the extent that anyone in Scotland is religious - which is actually very few and falling fast.
Meanwhile, nominally Catholic Ireland is rapidly becoming secular and pokes almost as much fun at the Catholic Church as the Ulster Presbyterians used to in order to get elected.
So the people of Ulster get the best of unity with both Scotland and Ireland in some sort of Celtic North-Western Union and remain inside the EU, avoiding that troublesome border and custom posts between the North and the Republic on the island of Ireland.
And the little Englanders get more or less what they've always wanted, having got rid of Scotland and troublesome Northern Ireland and still and having Wales to look down upon and regard as a possession to satiate their dreams of empire.
Wales are maybe the losers, being the junior partner in the Southern Kingdom but at least they get out of the EU and don't have to worry any more about that to do with all the EU regional development money they used to get.
And the result reverses 1500 years of Anglo-Saxon political, military and economic domination of the British Isles returning it to its old pre-Norman condition of an Anglo-Saxon south and a Celtic north and west. Ireland gets it's historic unity back; Scotland gets it's independence and everyone who wants to remain a citizen of a united Europe gets what they want.
Sooner or later Wales may realise it's in the wrong camp and the Little Englander's dream of their own Little England private estate will be complete - just so long as the Scots or Welsh don't want their Cumbria back or Cornwall decides it's better to be wealthy, progressive and Celtic than poor, regressive and Anglo-Saxon.