Can housing refuse notice extension?

I'm currently in the process of moving from a housing association house to private landlord. I gave in my notice for the house I'm in now and I have to hand the keys on 11th July. Me and my partner (Not living with me at present but moving together at new house) have a problem. He's not been paid his full wages and now can't afford the rent for new house. I'm petrified as I've got to be out this house in 2 weeks and nowhere to go to and I have a young daughter with me. Can I ask the housing association to extend the notice for a few weeks or can they say no and I can't argue with it? Help needed ASAP on this please, I'm going crazy with worry