I would apply now as a single person . Also you maybe able to get an advance , which is a loan payable over 10/12 months . Also moving out on Dec 16th hopefully this definitely happens but u dont have to wait for him to go . Also it is crucial you phone up council tax office as this is separate as you would need to claim council tax benefits and make sure you mention you are single as you will get i believe 25% discounted from bill( single person allowance).
Are you renting or is it a mortgage?