That's how insurance works. The OP is not personally liable because he wasn't driving and the car was being driven without his knowledge. His insurers will need to pay out because the car was insured by them at the time of the accident unless they can claim from someone else's policy e.g. if the mechanic had his own policy to drive customer vehicles which he clearly didn't.
The OP's premium goes up because the car was insured on his policy and a claim has been made against his policy whether he accepts fault or not. The mechanic failed to check that the car was road legal i.e. taxed, MOT'd and insured. It is the driver's responsibility to check these things before driving a vehicle in the eyes of the law and that applies to everyone although in the real world there are many circumstances when that doesn't happen.
To address the point about the mechanic having 3rd party cover on his private car policy - even if that was the case that wouldn't have applied here because that 3rd party cover only applies to privately owned vehicles and with the owner's consent not trade vehicles nor without the owner's consent.
