clp - To fly a complex aeroplane like Concorde (and they don't come any more complex than that) you need manufacturer support. Not only (as BA and AF did) to keep her flying, but also as part of the re-certification process with the CAA.
As I said before, there is no 'reduced requirement' for non-passenger flights. She would have to be fully re-certificated for flight (type certificate, C of A) or remain grounded. She would not qualify for a permit. Cricky, the CAA won't even let a Lightning fly again - and that is a tiny fraction as complex as a Concorde.