Health & council housing application

Hello
Could you direct me to a site which might help please if this is inappropriate for here? I have to find a home to rent in the next few months and currently in receipt of ESA Support and Housing benefit. I'm registered with the council's housing dept and was allocated a band some time ago. In view of my health deteriorating, I've reviewed my housing details in the hope of being moved up a band however have remained in the same band. Would it be wise to ask the council what their criteria is for their health and well being assessment ( cannot find on their website )and flag up that my health's deteirorated since my original application and/or do I need to review my health information again? Private sector renting is now unaffordable.

Any advice greatly received .

Thank you

Sue

I filled out a medical assessment form online for my housing application. I was then moved up to High priority Band B (If I remember right I also obtained a supporting letter from my GP)

Thank you Rachel, that's helpful.
Sue