For the visa, you need a valid, signed tenancy agreement, PLUS a letter from the landlord saying you have permission to live there with your fiance/partner after your visa has been granted (however long that takes).
Did the council explain why they are unable to provide a letter giving permission to stay? I'm wondering if it's due to an issue with number of people in the property, or for legal reasons, or if they're just being difficult about it.
Another option might be to find someone else you can both live with instead - another family member, or a friend, perhaps?