The child’s natural mother will automatically have parental responsibility.
The child’s natural father will have parental responsibility if he is married to the child’s natural mother at the time of the child’s birth or subsequently marries the natural mother.
It is more complicated whether you have parental responsibility if you are an unmarried father and you should take advice about your circumstances.
Other people may gain parental responsibility for a child in certain circumstances such as step-parents or grandparents.