Just a point to consider - your partner not only has an interest, but a liability in the property, and thus the mortgage payments, therefore you cannot simply add or remove people as you wish. Transfer of deeds is a simple conveyance that your solicitor will sort out for you - why are you here - that's what solicitors are for.
Land registry holds interetst in incumbrances on registered propert in England and Wales - i.e. Class G for a monetary interest - these have have to be valid to make any claim, and will be removed, again by your solicitor as part of the conveyance. Sort it out and go and see your solicitor. Good luck.