Aren't some people bloody inconsiderate? OK, it's only a car but even so the cost and inconvenience is big. If I'd reversed into someone's car I'd fess up immediately, leave a note and either pay or submit insurance claim.
Hayley - have you checked your car's fuses? That's almost certainly the cause. Without being too technical, LEDs have to be wired with a resistor in series with each one. If they're wired directly to the sidelights then as soon as one starts to light up it will be almost like a short circuit, which means that the amount of current exceeds the fuses rating. Commonly cars makers pair up electrical items and fuses, or put several devices on one fuse, which would explain the problem you have.
The chance of electrical damage is very very small indeed. Fuses are put there to stop such things occuring.
If you need further info then please PM me - My Dad's Astra is MkIV and I can get him to fax me over the fuses section of the manual.