This is actually quite a complex matter and so I would advise you to take professional advice from a solicitor.
A 'mortgage' is not a loan. It is simply a 'security' that the borrower grants to the lender in return for the lender lending to the borrower. So what?
Well, in your case, the effect of this, is that although you and your ex-partner share ownership and liability for the secured debt on the loan (the "mortgage"), you have assumed all the pain for paying for his/her half of repaying the debt. So he/she expects to get all the upside of acquiring 50% ownership without having to pay for it.
Morally, you should be entitled to that money back. But moral entitlement is not the same as a legal right.
Like I said...take professional advice. But I would be thinking of going down the road of seeking a court order for 'division and sale' of the property - a clean break where you sell the property and divide the amount received, or sell your share to him. But I think that, depending on the circumstances you could also claim damages for your losses.
What were the circumstances of the separation? Did your partner leave voluntarily?