"Surely each galley has its own refrigeration system?"
Indeed it has, Jeremy. Other than a massive galley power failure, I can't see how all galley chillers (cooling units) could be affected... unless cabin temps were high at some point (say, on an extended stopover in Singapore without cabin airconditioning). The chillers rely on there being a reasonably cool air temperature to start with. On our aircraft we try to cool the cabin before switching on the chillers, otherwise they will show signs of stress.
BA has about 9 chiller units per aircraft.
Some airlines have known problems related to cabin cooling. The all-cabin inseat video systems generate a massive amount of heat which aircon systems weren't designed to cope with. Sometimes it will be necessary to keep an aircon pack running in High Flow to compensate for this... with the aircraft not only suffering due to the extra weight of the video systems, but due to a a loss of thrust with the increased pnuematic (bleed air) demands.
Regards.
Q.