Hi Lucyc,
My understanding is that a parent could only be liable if a case for negligence could be established. Here it is the boyfriend's mother acting negligently.
I believe that third party Insurance claims can be made for crashes involving uninsured vehicles. If she was to have a crash, then the other party could make a claim through their own insurance using third party insurance. Their provider may require information from the uninsured driver and may have a limit on what can be claimed.
For further clarification, I would suggest getting legal advice and/or contacting a legal aid centre.