Since 1874, when a married woman registers the birth of a child, her husband is assumed to be the father, unless the woman says otherwise.
If the woman is single, or states a different father to her husband, then that man has to be present at the registration AND give his permission for his name to be included as the father.
But, the whole process is informant led; the Registrar just writes down what he has been told by the parent(s), and no proof is asked for.