Is there a single country with one livery for *everything*? As far as I'm aware, no. The idea an 800 will be in the same livery as a 377 on the West Coastway feels a bit nonsensical.
GBR will have control of English liveries only, so politically, InterCity services having a single English livery for services to Scotland and Wales is probably a no go - we're a 'union' and all that. It'll most likely be either done by Region (and IC) or sector - Suburban, Regional, Intercity - basically the German/French/Italian model.
There isn't an industry more in love with branding as much as the railways in this country, and the BR Corp Manual is held dearly as an icon; which gives me hope it'll be done well...
Sometimes you need a clean slate. You can't expect the railway to keep c2 flipping c - I don't think it can be anyway as a legal issue. There's too many brands, a unified railway doesn't need Southern, South West, Southeastern and Thameslink - it's all Southern, though I would expect Thameslink to be retained, if not, strengthened.