If parents separated can father take child without permission?

The father may take the child if and only if the child is not safe where it is and is happy to go with the father. You could leave a note and make sure that you leave a contact for the mother. Otherwise you may not. However the mother may not take the child from the father withot permission either. If you were to do this without good reason then it could be held against oyu in the court of law.