A mother automatically attains Parental Responsibility on the birth of her child. since legislation in or around 2014, a man attains PR by being married to the mother at the time of the birth, or by his name being on the birth certificate. If neither applies, he would have to apply to family court for PR. The court may order a paternity test.
If he succeeds in attaining PR, he will be entitled to 'all the rights, duties, powers, responsibilities and authority which by law a parent of a child has in relation to the child and his property.' For example, a right to decide matters of religion, schooling, health care etc.
Since further legislation in 2015, PR also includes a right of involvement in a child's life, which the law states improves a child's welfare 'unless shown otherwise'. The onus to 'show otherwise' e.g. that a parent poses a risk to the child, is on the other parent to prove at family court to limit or stop contact.
Because there is a presumption in primary legislation that a child's welfare is improved by having both parents involved in a child's life, there is an unwritten counter assumption that a parent who stops the involvement of the other parent, without due cause, is being emotionally abusive towards the child. This is often known as parental alienation or more recently as alienating behaviours.
Despite the presumption of involvement in a child's life, if they can't reach an agreement on contact (known as child arrangements), the father would have to issue proceedings at family court for PR/ child arrangements, which would need to be served on the other party.
Family law, particularly if your daughter was the victim of domestic or sexual abuse by the father, is complicated and I would advise your daughter to seek advice from a qualified family lawyer.
Hope this helps