Rent book? is it legitimate?

I have a week till im evicted so the my private land lady can do the house up to a safe standerd ,she is claiming we are in arrears but i am not and the council will not help despite us being a family due to this , they have asked her for proof off arrears but all she has is a rent book i have never seen with her signature on it ,it is a assured short hold , i just need to know does it count as proof off arrears as i paid her directly in cash at first but then started online transfer ?