Your partner was probably paid the standard rate of interest on mortgages (not repayment of the capital sum) if he was in receipt of income based job seekers allowance, he will not have to repay these interest only payments.
With regard to the property if two people are the legal owners, the agreement of both will be needed to sell the property, although if there is a dispute either owner can apply for a court order to decide how the property sale should be dealt with.
The major point here is negotiation, as has been stated by others, ask your partner to come to an arrangement with his ex-partner and co-owner of the property in how the sale will be dealt with, unless they agree there could be a problem. Even though your partner claims to have made all the mortgage payments, even if his ex-partner agrees to be removed from the mortgage documents the provider of the mortgage will have to agree.
His ex-partner may also feel she has made a contribution towards the mortgage payments by looking after the house & children.