Thank you everyone on here - including BobTheRocker - for the questions, ideas and answers. Saved me about £180, even with the exorbitant ;-) cost of Screwfix's replacement battery. I really am grateful.
Sparky - subscribed to diynot.com to thank you. You & Europlex just saved me ~£200 by posting how to change a faulty battery on a Scantronic 9651 alarm. Like the chap 3 years ago: £19.50 @ Screwfix for an identical battery, a little bravery when pulling the panel off in 'Installer Mode', and all...