Richard is correct and you should follow his advice.
Do not worry about your rights and responsibilities explain the entire position to your mortgage provider and offer to reduce the mortgage arrears as you are able and that you will maintain the mortgage payments if they will place the mortgage in your sole name. You will have to have an income acceptable to them and the existing mortgage holder will have to agree, they will, at first, not be keen on the idea and will try to bully you, do not put up with this it is a good offer and I regret to say that in my experience they will only be interested in money.