In England and Wales, civil registration of births, marriages and deaths was introduced in 1837. See Overlap between parish registers and civil registration records.
It took a while for the new system to be understood, so some parents continued to have children baptised and did not see the need to register the birth; others registered the births of children who had been born a few years before 1837.
Once things settled down, however, civil registration became widely accepted. Bear in mind that a birth could be registered within 30 days, so it might have taken place in the preceding quarter. Marriages were registered on the day of the wedding; deaths were registered before the burial, which might have taken place in the following quarter.
Double year dates
‘Double dates’ can be misleading, especially for inexperienced researchers. See Dates before 1751.