I turned my mains power off yesterday at my consumer unit and was
suprised to hear my burglar alarm ringing from the outside. Its never
done this before. I though that if the mains went off (powercut etc)
then the battery in the system would power the alarm. When I restored
the power the alarm stopped sounding.

I was going to suggest a flat battery in the panel, however.....

The battery cant be flat I presume as otherwise the alarm wouldnt
sound at all with the mains off. I took the battery out of the alarm
control box thingy and tested it with a multimeter. It showed approx.
12 volts so it cant be flat.

It still could be knackered - try turning the mains off again, and look to
see if the panels lights go off
It could also be a fuse for the battery has popped, so the battery is not
getting charged or used in the event of a power cut
If you take out the battery, then measure the leads that connected to the
battery, what do you get?

What make/model is the panel?

Surely this IS the symptom of a dud panel battery, and the Exterior bell box battery
powers the external sounder as it thinks its supply cable has been cut !

That too. It could be either. If the battery fuse has blown then the
SAB thinks the cable has been cut because it's receiving no power.
...

SJW
A.C.S. Ltd.