From previous poster:
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To those saying don't name the father - 2 things, he can go to the court to add his name so if he expresses a wish to be named it's simpler just to do it at registration (this doesn't give parental responsibility) and secondly if she needs to claim benefits other than child benefit they will seek information about the father - the state seeks money to support kids from both parents.
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Explicitly, putting a name on birthday certificate gives parental responsibility in law. How else do you think legal parental responsibility comes about? 
Unmarried parents cannot put down the other parent's details without the person being present. So actually, given the ex doesn't want anything to do with the baby, OP's daughter CANNOT add his name to the birth certificate. She cannot force parental responsibility on the father.
At no point has OP suggested her daughter will be applying for (or indeed in need of) state benefits. OP has clearly described the family home as suitable for daughter & grandchild to live independently.
Yes the father has options open to him to be added to the birth certificate - that involves court. And money.
As has been stated many times, grandparents (including the OP!) have no rights to a relationship with their grandchildren. CHILDREN have a right to maintain pre-existing relationships with their grandparents if it is in their interest.
No relationship with grandparents from before birth, no grounds for visitation.
@OP I wish your family every best wish for the future. I am sure you will do as much as you can to support your daughter keeping those ridiculous, awful people away from her and her baby.