I understand what you're saying here but the fact that the house has no equity will make no difference. It would apply in the same way as if you and your husband were divorcing and selling the house with equity in it - the courts would most likely award you a percentage of the house if it needed to be sold. Effectively, if the council were to approve your application because there is no equity in your house, they'd have to do this for everyone (whether single or married) who simply want to sell their property because they have no equity and wish to rent. There are many people in the negative equity situation at the moment but they're having to sit tight and ride it out. Your best bet is to rent somewhere privately for a while and re-approach the council at a later date. I don't think that even divorcing your husband would make the council accept your application.