What car, what engine, it takes a lot to slip a timing chain, so tell us if the car has been serviced as per manufacturer, lucky it was only £500....

So the last person to drive the car was the repairers driver. I assume it started ok after the bump and drove off ok so the slip must have occurred on the drive back or at the body shop. If the slip occurred at the time of the bump surely the driver would have noticed something was wrong in the way it drove or as injection doc says a warning light would have lit up and the driver would surely be savvy enough to know what that meant. To my simple mind you could present this logic to the repairers and ask them to make a hefty contribution or you'll seek legal advice and pursue them for the full damages.

The garage also have a "duty of care" so some responsibility lies with the garage. The car was driven away ok from the OP's house.

There have been a fair few incidents reported of timing chains or camshafts snapping after rear end shunts, including a few on this forum. Whether its coincedence or not requires further investigation.