Hi Lucy,
I'm in the process of doing this at the moment. The council will allow you to do this provided you get approval from the loan department to take over the loan.
Basically you just need to show proof that you can afford to look after the mortgage yourself. You will both need to engage the services of a solicitor as well, as the council will not entertain any application to change or remove names from deeds without sound legal advice being received by both parties.
Good luck with your application.