This is actually part of a TL of mine however work on it is going slow due to commitments in actual work.
Pretty much what happens directly relevant to this is:
1: England wins 100YW
2: Lots of English rebellions against French rule in the 16th century.
3: Scotland moves away from Franco-English sphere of influence (after being very heavily under it previously) and invades and takes northern England.
4: Around 1600 southern England finally manages to establish its nationhood as a republic.
And yes- this rebellion is quite an analogue to the Dutch rebellion (did I mention Burgundy is the major English backer?

)
Of course the world would be a very different place even apart from this, in the actual TL concerned this is very much the case (Crusader Egypt, Dutch-Burgundy super kingdom, capitalist revolutionaries, no reformation, etc...) but meh. That's another load of matters.
How would you see such a Britain developing?
I think this is really quite a interesting split; for one thing its far more 'natural' then the modern ideas of Scottish and English.
How would a industrial revolution take off with the capitalist south split off from the industrial north?