As a short-term measure the re-brand for a number of the operators would be relatively easy as they already feature large amounts of a neutral base colour (light grey or white), with just the end portions or doors differentiated in a contrasting colour, for example SWR, Northern, Thameslink, Greater Anglia, c2c, TFW, Avanti West Coast, even LNER and XC.
All of these could be relatively quickly stripped of their existing branding graphics, and a new corporate theme devised, perhaps with a subtle single-colour nod to the union flag design, a bit like MINI have often done, using shades of a colour that could be used to identify that particular operator. The overall effect would be quick and easy to apply, would unify much of the network instantly, and could still allow for the regional differences.
The treatment of the union flag graphic would be very subtle and not in the least 'jingoistic', I envisage it having the feel of the short-lived Virgin 'Flowing Silk' motif, with just a hint of the flag design within the design, positioned at the ends of each unit.
SWR for example would simply have the graphic applied in the existing SWR blue, covering the existing blue area. The SWR graphics would be removed and replaced by something like GBR South West with the modified Double Arrow logo. Job done!
A similar approach would be applied to the stock used by other operators.
Admittedly GWR, Scotrail and the new EMR would prove more difficult, but again a subtle flowing Union Flag motif using the exiting green, blue and purple schemes could be applied - with the legend GBR Great Western, GBR Scotrail or GBR East Midlands etc.
Local printed material would pick-up on these theme colours, and I could see signing nationally reverting to black on white.