or complain to the rac, get on the phone to customer services, tell them what happened, if they refuse, speak to the duty manager, start off calmly tell them what happened, start gettin shirty, if they say they wont do anything, ask to speak to their manager, and if they refuse to do anything, ask them for their name and position and tell them that you want the contact details for their manager and that you will be contacting trading standards, as they have damaged your car while they were working on it, and the service they are providing is not suitable, and your speaking to your solicitor. They should shat themselves nd agree to pay for the part and the work.
Also there is a high chance that you can take them to court and win the case as the damage was caused by the mechanics negligance.
Let me know how it goes it should work.