As others have said, the last airline will always be the passenger's point of contact.

The question of responsibility is different, and BA will liaise with QR to ascribe responsibilities.

Finally, again, people should note that when you get an airline to through check a bag on successive itineraries, you should always approach an agent at the transfer counter of airport where your second itinerary starts to ask them to scan your luggage tag receipt, otherwise your luggage will almost never arrive with you. That is because even though the bag has technically been through checked, the system of the second airline does not know to expect the bag on your flight.