If the battery in the system is dead then you may be able to disable your alarm by removing the fuse on the circuit powering it.
No, that causes the alarm (separate internal[1] siren) to sound, with no way to turn it off.
That's the whole problem. Power cut == internal siren sounding. Trying to silence the internal siren is not solving the problem, it's dealing with yet another symptom.
The second problem (well, symptom of the same problem) is that when the power eventually comes back on I've got 30 seconds or so to reset the alarm or the siren will go off again. This is annoying to my neighbours when I'm not there to fix it.
Dead backup battery in the alarm is the likely cause of all of it and last night's shenanigans have given me the impetus to sort it out. I just need the requisite powertools and beer.
1. Internal to the flat not the alarm box itself.