Fathers rights over children when mother remarries.

The situation: in the UK - abusive father (non married) leaves mother and two young children, He then decides he wants to have the children with him. The children utterly refuse to see their abusive (physical and mental) father. The court says he can't have any contact with the children for six month, during which the children will receive therapy. The father though can have a say in the children's schools etc. etc. What happens if the mother marries and a happy healthy family is created and the children totally accept the new man as their father (even insisting on changing their name). Is there some way the blood father can then not have a say in the children's schooling etc and be out of their lives for good?