Letter from tax credits – proof I'm a single parent

Hello everyone
It’s nice to be back here. Many things happened in my life recently. I found a fine job which relates to my interests finally, I am just about to start and spring sunny atmosphere made me feel very positive.. until today morning when I received a letter telling me to prove that I am no longer living with my ex …
I checked lots of forums, people are sometimes struggling with this for months. .
I think I do have some evidence, his payslips and most letters go to his new address. He’s also registered to vote there, I’m the only person registered where I live apart from old tenants but I think they already changed it for recent poll. We were both on tenancy agreement but when I went to council the lady said she will update the info for my agency on my behalf. Why are they telling me they have evidence that he’s living here?? It’s so scary and makes me feel like a criminal even if I know I’m honest.
He does pop in to take care of our daughter when I’m working on weekends and he keeps contact with her, he won’t really take her where he lives because he’s renting a room and there’s not much space to bring her in. He said he will provide all papers to prove he’s living elsewhere..
I just don’t know what to think about this. Has any one here had same problem?
Thanks