Abner, i apologise if i sounded like i was judging you - i wasnt. I have no right to judge anybody without knowing the full story and even then, i still have no right to judge anybodies situation.
Anyway, If the mother doesnt want any contact at all, then all monies e.g. child benefit, tax credit etc, should be made payable to the legal guadian of the child. All agencies, e.g. social services, school, GP etc, should be made aware of the mother not having anything to do with the child. The biological mother should then be aware that she would have no rights to request any information about her child what-so-ever - although this is not a legal binding contract.
If the father decides to go ahead with the adoption, then the biological mother can then willingly give her authority for the fathers patner to adopt her child. The biological mother can also willingly declare that she wishes no more contact with her child.
Good luck
Flower xx