Some aircraft have an oxygen ring main which can be used for medical purposes. It is supplied from oxygen cylinders. In addition, some aircraft use chemical oxygen generators and some use bottled oxygen to supply the passenger emergency oxygen masks. This depends on the aircraft type and options chosen by the aircraft operator.

Meanwhile, it seems like the problem the original poster is having is specifically getting two seats together on the upper deck (and it would have been a lot clearer to say that at the start). BA's seating together policies have nothing to say about seats together on the upper deck. I recommend they accept seats on the lower deck together and enjoy their trip.