I don't know the exact legal answer, but I went through something slightly similar. I had to leave my daughters father when she was only months old as he was smoking (and not always normal cigarettes) in the house while she was there despite my protests. He gave up his job while I was still on maternity leave (because he didn't like it anymore) and then proceeded to spend our bills money on fruit machines and beer. Although I loved him, my baby came first and I left.
Since then he has shown only intermittent interest, the odd cheque on her birthday etc. Then suddenly he decided he wanted to see her (told me by text message). So I checked up on the subject of access.
From what I can gather, access will only be granted if the court rules that a relationship between the father and child is in the childs best interests. If he would be jeopardising their safety, physical or mental health then it will be difficult for him to get access. (I know you didn't ask but just in case, as this freaked me out, he would have to prove your daughter an unfit mother to get custody). I was advised to make a record of any contact from my childs father, so they could see how dedicated he was to seeing his child, especially including any hostile phone calls/texts etc.
My child just turned 8 and he has never paid a penny towards her upbringing either. If your daughters ex is the same, this will also count against him. Remember though, only what you can prove is viable in court so gather as much info as possible.
I would definitly suggest you seek legal advice, but I hope i may have been helpful.
Best of luck!!