That will never happen...
The idea for he display on the Thames I could see happening though. There is NO way in hell people will allow an Ex AF Sierra Golf, French assembled Concorde to be in London. I doubt even AF would allow it since they still own their fleet, the same with BA. The planes are on "loan" to the museums. The best bet for return to flight from BA would either be Alpha Echo or Alpha Charlie.
You would need 100% support from EADs which owns the type certificate and engineering drawings, Rolls-Royce for engines (BTW there are no spare 593 Olympus sitting in boxes) and most importantly the CAA. Alpha-Foxtrot(BA) and Foxtrot-Foxtrot (AF) have the lowest hours but will never fly again. BA looked at keeping Alpha Bravo in flyable condition but the cost was deemed to high, the electrics still work on it as they bring it out for display sometimes.
If it does happen there will be no supersonic flights, no passenger charters as they claim. Please let's not use Vulcan XH558 as an example because that's an entirely different story