They're also a shareholder in IAG so they have an interest in keeping BA flying !
QR have a 20% investment in BA, so my guess is they've leased them on terms that won't break the bank. It would be in both parties interests to keep the operation running smoothly. Also the likes of Titan and other European charter carriers will be fully booked for the summer and BA cannot afford to keep cancelling flights.
One can see a smile on the businessman's face when boarding a QR aircraft even if it operates a UK shuttle service!