To officially remove her, a Land Registry Transfer document needs to be signed by her and your partner, which transfers the legal ownership of the property to your partner.
It would be normal for the Bank/B Society to grant their consent to the transfer, subject to the arrears being cleared, and for these arrears to be cleared shortly after the ex has signed but before dating the Transfer.
Unfortunately, to comply with the Bank/B Society's and Land Registry requirements your partner will need to instruct a local Conveyancing Solicitor to deal with this paperwork, and for him to liaise with the ex or her Solicitor concerning the signing and dating of the Transfer.
Basically, your partner's Solicitor will ask her to sign the Transfer and that he will then "hold it to her order" pending the clearance of the arrears an the completion of the Transfer.
Only by doing it this way, are you safeguarded in paying off the arrears and knowing that the transfer will indeed go ahead and get completed.
I hope this answers your question, and if so, I would be grateful if you could leave positive feedback.