UK Population Predictions

In my search for population details for Monmouth (town, not county) I came across On the Increase of Population in England and Wales by R. Price Williams, published in the Journal of the Statistical Society of London, Vol. 43, No. 3 (Sep., 1880), pp. 462-508 (36 pages).

A population projection of London and the England and Wales (definitely excluding Scotland and Ireland) takes the last census of 1871 base figure and projects ahead, in ten years increments, to the year 2181. So, the closest to us as I write is 2021.

How close was Mr Williams for us right now?

Mr Williams has the England and Wales population of 2021 at 91,753,000 (91.7 million) and, at the 2021 census, it was 59,597,542 (59.6 million).

You can all do the maths about the percentage difference and where it went wrong for him :)
Table from an 1880 statistical report with a table of UK population projections to 2181

The "immense population" of London in 1871 was 3,254,260 (3.3 million), and was censused in 2021 as 8,799,800 (8.8 million). What did Mr Williams predict it would be, 8 million. Wow, not bad Mr W.
Table from an 1880 statistical report with a table of London population projections to 2181
The first official census of Great Britain, including England, Wales, and Scotland, took place on March 10, 1801 under the guidance of a certain Mr John Rickman.
A table of figures showing the population of England and Wales, 1700 - 1801
A table of figures showing the population of England and Wales, 1801 - 1871
The pre-1841 censuses were simply headcounts. The data was collected on pre-printed forms which were destroyed after the details had been extracted and published in official census reports. There was no requirement to record details of individuals but some local officials took it upon themselves to do so. Some of these unofficial lists have survived and can be found in local record offices.

By 1901 the final tick column was "Deaf and Dumb, Blind, Lunatic, Imbecile, Feeble-minded", so there's that.

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