Thanks for your question.
First of all if if you and your ex-partner presently hold the house jointly (as joint tenants) then each persons share would pass to the other upon death regardless of any direction made in your Will. If this is not what you want then you should sever the joint tenancy by using Form SEV from the Land Registry (you will have to send it to them and if you have any questions about completing the form you should call their customer service number - they are very helpful):-
You will then hold your interests in the property as tenants in common and upon death your shares would pass according to your wills (or the intestacy rules). Your ex-partner need not sign the form provided you follow the instructions.
If you cannot demonstrate sufficient finance to receive a mortgage offer in order to remortgage and do a transfer of equity to you (ie. register the freehold interest in your sole name) then, unfortunately, she will be able to force the sale of the property by applying to the Court for an order for sale. These orders are seldom refused but the division of the proceeds of sale are usually subject to negoatiation.
Although there is a presumption (in the absence of any express agreement) that you each hold a 50:50 share. However, if you financed the purchase of the property and maintained the mortgage payments/bills (albeit for a short space of time) then you will certainly receive a larger share of the proceeds of sale.
You should shop around to see if it is possible to get an offer from different lenders, if you can also bring a guarantor in then this would make you more attractive to lenders. If you think you manage her and delay her taking legal advice on her position then this may also be a further strategy you could avail yourself of.
Sorry it couldn't be better news, but I hope you agree there is little point in my sugar coating your position.