We are familiar with the census form structures for 1841 onwards, and each decade the form undergoes changes.
The parish were sent copies of the parliamentary act and the schedule. This made it’s way to the Overseer of the Poor and then subsequently to the Officiating minister of the parish who was tasked with providing the number of births, marriages and deaths. Having made the official submissions, it depends on the incumbent if a copy or the details was retained.
The image below is from the Surrey parish of Compton. The page is from the parish register, where there are entries for births, marriages and deaths, and where the officiating clergy retained the information relating to the 1801 census – you can see a better copy of this below:

Compton Parish Records – Surrey History Centre; Woking, Surrey, England; Surrey Church of England Parish Registers; Reference: COM/1/2

Surrey History Centre; Woking, Surrey, England; Surrey Church of England Parish Registers; Reference: COM/1/2
As you can see, there is no individual specific data, but the information there is, enables us to have a snapshot of the village, which is replicated across subsequent census.
At first glance, it seems quite random that the rector would have chosen to have kept the information in this register, until you understand the context of the questions asked and the individuals charged with providing the information, which we looked at in the first post in this series.