Hello Lis234,
I have had a lot of realings with Parish Registers over the years and what you describe is typical. On 1st July 1837 details of parents, occupation, etc had to be recorded on pre-printed forms supplied to the church. Prior to that it was down to the cleric of the day to write down, illegibly if posible, the details of who was being baptised/married/buried.
Parish records started to be kept around 1570 which gave the date, the child's name and the name of the father. Not the mother, she wasn't deemed worthy of mention then. In the 1600's the mother's name was added, except for the Comonwealth period (Civil War) when it reverted to father only. Normal service resumed at the Restoration in 1659 and continued until around the 1800's when sketchy details were added - parent and later occupation. This became a requirement as from 1837.
There will be no further details to be had from parish records as the recording was, at best, haphazard. They are, however, the most accurate guide to ancestry as they are records of the time and have not been mistranscribed since. That's not to say that the church records themselves were always accurate but it's the nearest one can get.
Hope this is of some use
Regards
AJ
