CB
When you say that no father's details have been recorded, are you referring to the birth certificate? I have checked the 1881 census and there is a 4 year old Isabella Hogg living in Eltringham Colliery whose birth place is given as Mickley. She is living with what would appear to be her mother - Mary J Hogg, age 23, unmarried, outdoor work (ag lab), born Scotland - and her grandmother - Mary A Hogg, age 50, widow, outdoor worker, born in Birtley, Northumberland.
Mickley would then have been in Hexham Registration District and there is a birth recorded in the September 1876 quarter in Hexham under reference 10b 294. This would put Isabella's birth at 4 at the time of the census and consistent with the above information. The fact that her mother was unmarried will probably reveal that no father's name was recorded on the birth certificate but you will need to order the certificate to find that out for sure.
Regards
Gordon