Lima Juliet, the Ford Prefects are still 'aircraft registered in the United Kingdom' nonetheless.
Thus to fly them for ab initio flight instruction, a civilian pilot will need a Part-FCL pilot licence, valid Part-MED medical certificate, SET Class Rating, IR to fly other than in VMC, Aerobatic Rating to fly aeros and (presumably) an FI certificate. The SET Class Rating, IR and FI certificate will need to be revalidated by civil Examiners, as will the Part-MED medical certificate.
Of course if the RAF still had its own aeroplanes and QFIs, things would be much simpler....
No matter what the calibre of the civil pilots employed by an MFTS contractor might be, the issue is that the legal requirements of Part-FCL cannot be ignored for commercial convenience and the contractor's bottom line.