At privatisation in 1996, BR had no experience in proper high speed rail (as in Shinkansen, LGV, NBS etc).
IC250 never got off the ground and would have been small deviations of the WCML, not reopening the GC.
TV4 is all we have to show for the intended WCML upgrade, and still at 125mph.
HS1 was designed to largely LGV standards (track, OHLE, signalling), by a separate government-owned body (with access to private capital).
Partly this was influenced by the interface with LGV Nord and Eurotunnel (which adopted French technical standards).
HS2 is following a similar path, and the senior people in HS2 Ltd seem to be ex-BR and consultancy types with major infrastructure experience, including abroad.
There was no chance that "BR" would have been given the job of building a mega-£billion new line as it didn't have the capability, and no credibility with the Treasury.
BR and its successors have enough to do with the day job.
We'll have to see what role, if any, Network Rail takes in operating and maintaining HS2 (they do that for HS1 under contract, not as part of their normal licence).
And as for what colour their HS2 trains would have been painted...
They will be painted whatever colour is agreed between the DfT and the WCP franchisee (who will also be running the classic West Coast network of Pendolinos).