I have seen a birth certificate once and a death certificate of a young child where it said "deceased" with the name of the father (1880's, 1890's England). Would that be an exception, or would it be usual?

I have a certificate of a birth in september 1896, that wasn't registered by the mother until July 1897. She was often quite slow in registering births, but I hadn't seen one that late. The boy died sep qtr 1897, so I think birth and death were registered at the same time.

I'm trying to figure out if and when the father had died (can't find a death record at all). If he died between the birth and the death of this child, how big is the chance the death certificate would tell me?

Loes
ADDED:
The birth certificate just states name and occupation of father. Could I count on it that he was still alive at the time of birth at least?

The excellent BMD tutorial gives what information can be found on English certificates:

http://home.clara.net/dixons/Certificates/indexbd.htm