Hello Lee,
Try a local electrical outlet or wholesaler (sometimes found on out of town industrial estates). The battery is a NP1.2-12 Yuasa (or similar) 1.2Ah 12v sealed lead acid battery, or you could go for a higher rated one at say 2.1 ah whichever you can afford. Do a quick 'google' or 'search' for either 'yuasa batteries' or 'alarm batteries' to get an idea of what they look like before you go shopping, it's quicker than describing it here.
If the led's (lights) are coming on at the detectors it means that the control panel is supplying them with power, so that particular fuse hasn't gone. But it doesn't say anything about your existing battery which is more than likely doomed, and the quicker it's out of there the better since it can damage the control panel. Batteries start at around 12 to 15 quid.
Our intention is to silence the sounder, check the keypad fuse, downpower the system and hopefully bring it back to life. (it's probably a 1amp glass fuse, but it's worth getting a 500ma as well. These fuses are much smaller than the normal domestic 13amp fuse. It's worth having a few of these handy, they're only a few pence each - google 'control panel fuses' or something similar just for a glance) so it's 1 amp and 500 milliamp glass fuses. Two lengths of cable, about the thickness of alarm cable, to reach floor level from the control panel. If not alarm cable, 2 core flexible table lamp cable will do.
We'll sort that bit out first and go from there, hopefully without interruptions, since we need to take it one step at a time, since we are still in the dark as to what we may find. Fingers crossed then !!
Thanks for your patience Lee.
Take care mate
Chain Daisy.