When you file a consent order you have to send in a \"Statement of Information\" on financial facts in outline. On the back of the form you have to say whether the mge lender have/not objected to the proposed transfer of interest in the house.
The problem with a mge is that it's a contract. The lender on the one hand, you two on the other. The basis is that you are both \"jointly and severally\" liable to pay it. As a lender, you have two possible targets to get your money. Why would you willingly give up one of those targets? You see the problem from their PoV, suddenly it's not quite so unreasonable.
The thing to do is to convince them that the Ex isn't necessary, or even remge with just yourself as sole borrower perhaps.
But as Fiona says, if all else fails, you just have to \"make best endeavours\" to get the ex off the mge hook, best you can do.