The funeral payment mentioned by kathyan will not cover the whole of the funeral costs. ANY savings, or money in your father's name, will be taken pound for pound from any payment made.
Single persons Council Tax benefit isn't a qualifying benefit either I'm afraid. If your father owned his own house this too would be taken into account.
You are allowed to apply for a Funeral Payment up to 3 months after the date of the funeral.
Sorry this will not be what you want to hear.
You'll find funeral directors are use to your situation and I would advise you to talk to them.
Regards