I am a civil servant but not a registrar, but I was really interested in your question so did a bit of research. All the (UK) local authority sites that give information about the registration process say pretty much the same thing - Ive copied below typical information (from Waltham Forest):
The Registrar will see you in private and will ask questions about your baby and both parents.
The Registrar will put the information on a computer file and will write down the details in the birth register.
You will be asked to check the information in the register and to sign that it is correct. Please check the information very carefully. It is not easy to correct the information after you have signed the register.
The registration will take about 30 minutes.
What information will the Registrar ask for?
About your baby
The place and date of your baby's birth. If you have had twins, triplets and so on, we will need the time of each baby's birth.
Whether the baby is a boy or a girl
The baby's first names and surnames.
About you - the baby's mother
First names and surname. Your surname before you were married if you are or have been married.
Your date and place of birth.
Your usual address on the baby's date of birth.
Your job at any time before the birth. (You do not have to tell us this.)
If you were married to the baby's father at the time of the birth, the Registrar will ask for the date you were married.
The number of children you have had.
About the baby's father (If you want their details to be included in the register)
His first names and surname.
His date and place of birth.
His work at the time of the baby's birth. If he was not working at that time, his last job.
I was really shocked about what you had been asked and would certainly make a complaint to your local council (who is the employer) about the highly personal and irrelevant information requested by the registrar. I wouldn't let this go...oooo....I'm really cross myself now! :)
Research/parent/grandparent who's done this loads of times.