Hi Ted, As im not in your house i can only guess, but well done for giving me good info on your panel so that i may help you.
OK Ted the only obvious reason why this is happening, is that your burglar alarm mains is wired into your house lighting circuit, well one of the two 5amp circuits you probably have. When the bulb blows, it is probably tripping the switch in your consumer unit, at this point your battery in the alarm panel should automatically take over. The only reason why that hasnt happened is because the glass 1 amp quick blow fuse has gone in your panel. Replace it. Please dont do what others do on this site, and look at it with your eyes, there is no way on earth you would be able to see a broken fuse with your eyes, Replace the fuse and your problems will be over. The battery will charge back to normal in about 24 hours dependant on its amperage. Im sorry you have been ill advised by death, who thinks he knows a bit about alarms.
Regards
Nick 07842 480037
Nick, January 2010