Plastic mountings on bikes are crap. Lights, pumps, locks, whatever the item, the plastic mount that came with it will be a prime suspect for breaking prematurely at some point. And that's exactly what happened to the mount for my cheap ebay light (I seem to break expensive ones just as easily I should point out).
I hadn't liked it on the handlebars anyway. It's big and ugly but does throw out a huge amount of light and poundshop batteries last for yonks in it. So I decided to find somewhere else to diy mount it as a temporary fix whilst I um & ar about playing with cree lights of some sort.
A quick search in the bit & bobs tin found this:
It's probably some kind of reflector mount I've removed in the past, I'm not sure. A quick look at the front of the bike and it looks like the mudgaurd mount on the fork will be a good spot.
I threw away the broken mount and drilled a hole in the bottom of the casing. Then mounted it on the bracket with a small bolt. This is the most important bit -I put a piece of innertube between the bracket and the light mount to dampen any vibrations. I did the same between the bracket and frame.
I know it's a bit rough and ready but it works and it's solid, plus it gets the light out of the way where you can forget about it until you need it. Maybe at some point I'll tidy up the bracket a bit with either a polish or a coat of black paint.