I am separated from my 2 year old daughter's father. He is signing unemploymnet benefit. I was claiming income support and have been offered work but can't afford the childcare costs. Could I make the father look after her.

No, you can not "make" the father be the baby sitter. You may ask him to, but you can not make him.

Separated? Does that mean you are still married ? Is he on the birth certificate ?
Is there any custody order in place ? Is there any child support order though the courts ?