It sounds like your alarm doesn't have a backup battery, so when you turn back on its power, it immediately goes off. If it had a battery, it shouldn't have gone off when the power was lost.
If you know your code, type it in to stop the alarm. If you don't then you should really get an alarm engineer to come in and sort it out for you.
There is usually a fused spur (a box a bit like a light switch, but that has a fuse in it that you can remove), near the alarm panel. If you take this fuse out, you should then be able to turn your lights back on without re-powering the alarm panel.
Hope this helps (and isn't too late - you must have been sat in the dark for days if you have not already got this fixed!)
Chris
Chris, June 2007