Applying for permanent residence and becoming homeless?

hi. could anyone give me guidance? I am an eea national (czech) and i am applying for permanent residency for my husband. We need to move out from our home in a few weeks and asked the council for help. they advised us to make a homeless application, but i am worried because i dont want this to affect my husbands application. we have a small child and have no where to go. can anyone give me advise, please? thanks so much.