Yes, under the 1874 Act. Between 1837 and 1874 if the mother informed a registrar of an illegitimate child's birth and also stated a father's name, the registrar could record him as the father, although he may not have actually been the father.
This applied until The Registration Act of 1874 which stated:
"The putative father of an illegitimate child cannot be required as father to give information respecting the birth. The name, surname and occupation of the putative father of an illegitimate child must not be entered except at the joint request of the father and mother; in which case both the father and mother must sign the entry as informants" The Act came into force on 1st January 1875.
Stan