It depends on whether or not the Father has parental responsibility. A Father only has PR if he is married to the mother when the child is born or has acquired legal responsibility for his child through (a) (from 1 December 2003) by jointly registering the birth of the child with the mother (b) by a parental responsibility agreement with the mother or (c) by a parental responsibility order, made by a court.
In England & Wales you cannot remove a child from the UK for longer than a month without the consent of all those with PR for the child or the leave of the court. If the Father doesn't have PR he can apply for it at the same time as an order to prohibit the move so as too avoid the hassle and expense of last minute court applications it is a good idea to sound out the Father and get written agreement.
In the event he doesn't agree and the matter goes to court it is unusual for permission not to be granted to remove the child for the UK as long as plans for accommodation, finances, education, work, contact etc are well though out and concrete.
The exception to this is when the child effectively lives between two homes and spends their time more or less equally with both parents. in this case the judge may rule it is more stable and secure for children to maintain their existing bonds with friends, family,school and remain in the UK providing the other parent can provide them with a home.