This is probably being claimed under the Localism act 2011, your ex-partner has probably convinced his solicitor that he needs to protect his interest in your property, which could lead to a notice appearing on your title register that he has an interest in the property, which could cause you many difficulties.
If you object to this notice appearing it will probably go before a land registry adjudicator to decide if his claim can be justified, and unless he is able to show he has contributed towards the property, which you claim he has not, the registration of an interest will not be allowed.