Yes, provided all the council's requirements have expired through time which they should have done given the dates.
You can do it yourself easily with TR1 and AP1, if for no money then you also need to send an SDLT 60 form certifying it's exempt from stamp duty.
The deed of trust should have been tied to the fact you are both on the title register at present so it will be ineffective if the register is changed into your sole name.
Have a check and if not then just do a simple deed revoking the deed and send it to the Land Registry so it's been lodged and there's proof that things have changed.