In my opinion, the only way of buying a new property is to use the savings to clear the negative equity, sell the existing house, clear that mortgage and then your boyfriend applies for a new mortgage in his own name. With a bad credit history, you're not going to be accepted. Even though he's only a joint name on the existing mortgage, most lenders will count the full mortgage as a liability of his own, so it will pretty much scupper his chances of getting any realistic amount while it's still there.