My god some of you are so alarmist it hurts to read these posts.
Not really when you consider that if anything happens due to attempts to remove the vehicle that causes more damage insurance companies can and will deny a claim for the damage.
I've seen/heard of instances where Insurance companies have argued about whose responsibility it is to separate two cars after a minor collision because one car had a tow ball that was caught up in the other* - neither company was happy with authorising the actions needed because the moment they did it put responsibility for any further damage (and opened up an argument about when the damage happened) on them, rather than the other other company.
If someone tries to remove that car and it slips and hits the building (again?) that's going to be a possible additional claim for damage, so no professional will want to touch it without knowing they will be covered by the insurance company, and the insurance company will want it done properly - even if that means involving a crane and full recovery crew.
I'm guessing the OP is going to want the stone steps put right, which on it's own is another potential thing for the insurance company to quibble over (where these stones knocked loose by the initial incident, or by the attempt to drag the car free).
Personally this is a situation where I wouldn't even have hesitated to get the insurance company involved, as the chances for something to go wrong and ending up with the innocent party out of pocket are too high, and the longer between the incident and the insurance companies getting involved the harder it is likely to become for the op and the driver to get them to cover it easily (as from memory you are meant to inform them as soon as possible).
*I actually saw one example on a police programme my father was watching the other week.