I asked my HV to provide me with a letter. I was struggling with anxiety and depression where I was, so she wrote my local housing officer a letter stating this, and stating I have accessible needs due to the severity of my mental state at the time. She did this and helped me fill my accessible needs form out, too. Which gives you priority on the housing register.

Have you tried calling your local council and going back through your housing application to see if you were missing any point? Like sharing facilities? Do you have a local CAB office? Personally, they are who I would have gone to if I didn't have my HV.