What are the sums like? As in, how much is house worth, how much is outstanding mortgage, will there be any stamp duty payable, what is your status as a purchaser (i.e. ftb, second time buyer, investor?), can you get a mortgage and if so for how much?
Ex partners share is presumably 50% of the equity in the house ( i.e. the capital value of the property less the mortgage) so new purchaser will either have to take over old mortgage ( may or may not be possible) and raise cash or both of you will remortgage to pay off old mortgage and raise cash.
Do the sums and post back.
mf