Hi Suzanne
I'm no legal expert, but unless the father was present and willing to have his name added to the certificate, I think that the father would have to be left blank.
You say that the registrations are on the same page? It would be interesting to know if they are next to one another on the page (if it is a B'ham cert, then if you ring John Yates at the reg office, he may be able to tell you). My guess would be not - they could be up to 6 weeks apart (which is I think the time you have to register the birth). Also, when you get the second cert, check that the birth dates are the same as the second one might have been 'late' and had to have the date adjusted to stay legal.
Thinking laterally for a minute - what is the reg date on the cert that just has the mum on? Is it soon after the birth date? Could it be that she was desperate to register the baby because it was poorly. If the father was out of town he couldn't have been added in. Or maybe they had had a tiff and wouldn't acknowledge the baby and she simply went to register the baby wihtout him.
You may never know the reason.......