If you get consistent splits of that nature, you should really look into breaking into two countries.
This point in particular resounded with me:
> The referendum has underlined the social and cultural gap between London and provincial England.
This applies pretty much everywhere. You have the temperate / urban / high-immigrant liberal places, and the more desolate / isolated / sparsely populated / resource rich conservative places, and for some bizarre reason we still keept forcing them to operate under one government.
I have long advocated that in the era of NATO, the UN, and nuclear arms that massive states on the scale of the US or what the EU was designed to be (effectively, over the long term, another US) is counter to all notions of democracy. You only need an independent state so long as it can assert its own borders and have enough economic significance to have bargaining power in international negotiations.
The Northeast Corridor in the US, the West Coast from SF to SD, the Rust belt, and the Carolina's are examples of fairly homogeneous societies, that would make a lot of sense being their own countries, and are all fairly distinct, but would all have significant enough size and GDP to still function easily as first world countries.
Texas is an example of the opposite problem. It has 4 liberal cities surrounded by cowboys. You would almost just want to make 3 cities (Austin / San Antonio are close enough to form one) that are independent states that behave like Luxembourg by being landlocked around the Midwestern Confederacy of Rednecks that spans from the Carolina's to the Rockies.