I think you should do whatever's necessary to get the letter and agreement from the council (writing to them as Tremula suggested is a good idea), and if they refuse to play ball then you might have to take drastic action. Which probably means moving out. It is essential that you don't lie on your application, but you need to prove that you have a place to live and permission to live there. So if you can't get the necessary permission from your fiance's current residence, then you will need to find someplace else. There's no requirement for you two to live together for the fiance visa, so it would be OK if he stayed in his place and you stayed somewhere else for the duration of the visa, but you have to tell the truth on the application. When it comes time for you to apply for your FLR(M) the same things will be required, so it's best to get all this sorted out now.
IIRC, the person on this board whose fiance's landlord refused to write a letter ended up staying with her in-laws until she and her fiance found their own place. Not ideal, certainly, but unfortunately sometimes necessary.