Generally in the UK if a father is proven to be the father, then he gets immediately Parental responsibility which is similar to legal custody. After that he can file in Court for contact order/ visitation/. There is no strict conditions how much time to be granted.
According to the Children Act ,
(1)In this Act —
“a contact order” means an order requiring the person with whom a child lives, or is to live, to allow the child to visit or stay with the person named in the order, or for that person and the child otherwise to have contact with each other;
“a prohibited steps order” means an order that no step which could be taken by a parent in meeting his parental responsibility for a child, and which is of a kind specified in the order, shall be taken by any person without the consent of the court;
“a residence order” means an order settling the arrangements to be made as to the person with whom a child is to live; and
“a specific issue order” means an order giving directions for the purpose of determining a specific question which has arisen, or which may arise, in connection with any aspect of parental responsibility for a child.
I have seen many orders from two times direct contact a year to shared residence plan.