I doubt whther you can claim compensation, but all these outfits are licensed by OFT and (in theory) can lose their license. Some also belong to another trade body. You can complain to either organisation, or to Trading Standards. You should also go to the Information Commissioner about the confidentiality breach.
You should certainly complain. What they have done is not only a breach of your confidentiality but a totally incorrect statement of the law. No way can your mother lose her home if the debt is in your sole name and you are not an owner of the house.