Until quite recently payments under bastardy or affiliation orders were
normally made through magistrates' court offices. This provided a means of
tracking payments and verifying arrears when those concerned on both sides
did not usually have bank accounts.
As the name of the father is known, it should be possible to narrow down
the possibilities by establishing which men of that name lived during the
relevant period in the Petty Sessional Division of Southport. Of course
this could be a mighty or a manageable task, depending on the frequency of
the name. It could be worth seeking information from the court records
there, if they survive. At least divisions then were somewhat smaller than
they tend to be now (at present there is a Division of East Kent, for
example). After the first world war, most men of full age appeared in a
register of electors.