Ermmm im not sure babe!!
Im on the housing list at my local council & it's loooong!!
They take into consideration things like it being unsuitable & overcrowded. But just because you have a LO they wont bump you up the list

Aslong as youve got a roof over your head your not really seen as an emergency!!
What id suggest is to look at private renting. If your OH is working then you should be able to get a deposit together. Some councils help with that. Also housing benefit will help cover your rent. Thats what I intend to do
xx