Getting council or housing association houses these days is very hard, even harder if you are private renting as the council usually regard you as being adequately housed, and you will almost always be pipped to the post by someone on the homeless list.
I got a housing association house three years ago. Where I live the council dont have a list, they only house people who are homeless or facing immediate homelessness. I lived with my mum (with my 3 children) as I had been caring for my dad before he died, and my mum wrote a letter 'evicting' us and we were housed within 2 weeks. She would never have actually evicted us but I wanted to live with my (now) husband, who is severely disabled, and even though he got maximum medical points for housing, our local council wouldnt move him here (he was living in a different council area). As soon as I was offered the house I had a meeting with the housing officer for my housing association and he asked if my partner would be moving in with us and I admitted he absolutely would be once he handed in his notice on his bungalow, and the housing officer said that was brilliant and it wasnt often they got to house couples with children anymore! So it was a win win really, we got to live together as a proper family, and his disabled adapted council bungalow could be re let to someone who needed it!
I would definitely talk to Shelter, they were brilliant when I was having housing benefit issues years ago (when I privately rented)
You say you are worried about reporting her to the health and safety for the mould for fear of being evicted, but in all reality of she did evict you for this your council would have a duty of care and would be forced to house you! So that may not be such a bad thing really!!