Child receives chemo for chronic condition becoming homeless?

Can that happen? I have been trying to speak with the hospital to explain the situation but it feels like no one cares.

Since the beginning of January, I have been declined so many times for private property. I can prove I can pay rent, but the downside I am a single parent, so I get why they would prefer 2 adults instead of one.

I have spoken with the council but they said the only thing they can do is move in banding for social housing if I can prove the house condition affects my child, which I am trying to but the hospital is so slow. And even with proof, there's no guarantee of anything. I don't think we will be a priority either. I have spoken with so many different people, secretaries, and consultants, they keep postponing writing me a letter stating that my immunocompromised child can't live like this let alone become homeless. I don't know what else to do.

Yes, I've tried Shelter, no response, I've spoken to a solicitor about the housing situation. Told me I needed to wait until the last minute to become homeless, so the Council could help. I don't want that. Spoke to Citizens Advice, not helpful at all. My child is in therapy as well, surely she shouldn't go through witnessing becoming homeless for someone's help?