If a unified branding is to be used, I think it would be most effective if it could be introduced as quickly and cost-effectively as possible. It has to be conceded that re-branding of Scotrail, TfW or London Overground is very unlikely, so as the new GBR services are likely to run mainly within England, I would personally suggest a livery with a nod towards the England flag, and I don't mean the cross of St. George everywhere, just a subtle use of red highlights, together with whites/greys and silvers.
Much of the rolling stock now has a base coat of white or light grey, so it would just be a case of replacing the multitude of colours that abound at the moment with reds and greys and using the Rail Alphabet consistently. The new red/grey areas can be fairly random, and, for the time being to make the transition effective and as quick as possible, the red/grey areas would literally replace the existing colours, for example the blue areas on Northern and SWR would be replaced with reds/greys. The overall effect eventually would be to have all trains in a livery very similar to the current Greater Anglia.
With the colours used in this way, I do't think anyone could accuse them of being 'jingoistically English', in fact most people wouldn't really read anything into it at all - but it would bring some much-needed consistency to the fleet and help to quickly establish a 'brand' in the eyes of the public to signify change.
As a graphic designer myself, such a change would not only provide some much needed visual consistency to the network, but it would also ensure that any change in contracts or re-allocation of stock doesn't entail un-wanted and unnecessary expenditure on endless re-branding.
There are a few fleets where this isn't so easy (think South Eastern and gWr), but many of the existing schemes could be adapted quite quickly and easily - LNER, Greater Anglia (already done!), Northern, SWR, Southern, XC, Avanti West Coast, c2c etc. The roll-out would be relatively easy!