On the subject of illegitimate births, if the father is not named on the birth certificate what is the possibility of finding out who he was? And how could I find out?
My great grandmother was born in 1865, at Helston workhouse, father not named. 
You can hope that a baptism record will name the father? Some vicars named the culprit!
Or that a Bastardy Order exists, requiring the father to pay what we now call maintenance.
I attended an Anglican Christening a few years ago, and had an interesting conversation with the lady vicar.
She said that a Christening and a Baptism are in fact 2 distinct services! But that in nearly all cases, the baptism follows immediately after the christening, without a break.
The Christening part is giving a name to the child.
The Baptism part is welcoming the child (or person) into the family of the Church.