As you say they go back to 1837. I think the answer must be two or three times your estimate. All those alive in 1837 will have had a death and a fair number a marriage. All the people born since will have had at least two entries and most a third plus all those alive now will have had a birth and again a good number a marriage or possibly two. I was born in 1943 but can still obtain certificates back a further 4 or 5 generations before me. I think that you have grossley under estimated, probably 200 million
The Registrar general compiles a report every year Annual Report of the Registrar General of Births, Deaths, and Marriages in England and Wales
The findings for 1901 give figures such as
Population March 1901 - 32,527,843
Population was estimated to have risen to 32,621,236 by the middle of the year if emmigration & immigration were allowed for and deducted.
The number of marriages per year from 1897 to 1901 averaged at 16.05 per thousand of the population for each year.
There are numerous other figures given including birth & deaths (21.0 per thousand of population each year for period 1837-1901) for those who are interested in studying the figures.
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