fluffyjumper, that is unlikely in this case, as the resident mum would have to claim she doesn't know who, or where, or how to trace, OP's DH.
The fact she is receiving maintenance means that either the child is not adopted, or that the resident mum would be in contempt of court. At application to court for adoption, all possible ways to find the birth parents must be made, including via their NI number etc if claiming benefits. The court could certainly get this info from the CSA/CMS if applicable, and wouldn't grant the adoption order until the birth father had chance to object. Unless the OP's DH pays direct into the mum's bank account, and she lied in court, in which case she would be in deep deep shit.
But if OP's DH applied for contact at any time, the courts would know this, and therefore would not grant an adoption order.
Adoption isn't easy, as you know, fluffy, even in step-parent adoptions, which is why sometimes step parents will apply for PR, in their own right. That is different to adoption.
So, actually, OP, it's entirely possible in your case that step dad had PR granted by the court. It's entirely possible that the people with PR (mum and step dad) have changed the child's surname. It's unlikely the child is adopted without your DH knowing.
He can apply for PR himself.
Whatever, he should pay for his child, and I think resenting the money going to pay for his child is bad taste.