If all operators/regions are to get a standardised livery, I don't think this should be based on the flag. Looking at nationalised railways in other countries, very few brands are based on their flags. I think the NSE blue/red/white is quite jarring (and am not a fan of the London Underground livery either). None of the current privatised operators use a red and blue livery - Chiltern dropped red from theirs, and their current branding does look a lot better.
For a nationwide livery/brand, something more retro would make more sense, similar to GWR and EMR. The UK was one of the first countries to have a rail network, and has a lot of history around the railways, so this should ideally be reflected. A dark green livery would work well, having been used a lot historically - and in addition to GWR, is also now used by Caledonian Sleeper, Avanti, London Northwestern and Southern. Also, as the livery is likely to be used mostly for intercity/regional/rural services, a green livery would blend in better with the countryside compared to red/blue.
Alternatively, if they want to go for something a lot more modern, I quite like the idea of an orange livery, as used for paper tickets (as well as the Network Rail brand). Something similar to the old TGV livery could work well. I've also not seen Grand Central mentioned in these discussions - as a simple but unique livery. Perhaps an orange version of an EMR/Gatwick/ScotRail style livery for most services, inverted to something similar to Grand Central for intercity?