Ok, this isnt a legal answer, but why isnt your new partner paying 'rent' which will help pay the mortgage if he's living there with you?
I think you need to make your ex an offer to buy him out of his share of the house and remortgage either on your own or with your new partner. Depending on the value of your property, the amount of mortgage etc, the offer to your ex could actualy be nil i.e. "you agree to sell me your share of the house and I wont chase you for mortgage payments etc"