Writer joemjackson, in chapter 157 of his delightful "Harry Does Different" collection (story #12416998 if you don't already know), took a much simpler and more direct approach to trying to estimate the total magical population of Great Britain. He found that in the US 11% of the general population is between the ages of 11 and 18 (the ages range of Hogwarts student if we ignore poor, dim-witted Marcus Flint who had two seventh years). Assuming this carries true for magical Britain as well and estimating that there are 336 students currently in Hogwarts, he calculates the population of magical Britain to be roughly 3050. Not incredibly out of line with my calculation of 5100 in the previous installment.
Now, if you look at the reviewers for joemjackson's work, there are a couple that point out some interesting things. The one I want to mention here, because it got me thinking of a different approach to this estimate, was posted by hakon2feb. He/She points out that magical Britain had been subject to two devastating wars, Grindelwald's war followed by Voldemort's just 30 years later and this may have an impact on the population that would impact using a modern population profile, i.e. people not having children during wartime.
Memory drew me to a real world analogy. Real world Britain suffered through two devastating wars in a close sequence, WWI which ended in 1918 followed 20 years later by WWII. To further the similarity, in 1940, England was in the midst of the Battle of Britain and on the very brink of defeat to the attacking Nazis, just as magical Britain was on the verge of defeat by Voldemort in October 1980 as we are told in canon. This lead me to another method of estimating the population of magical Britain: by comparing the birth rate in Britain in 1940 to the size of the general population we can establish a proportion that when applied to the number of births in magical Britain in 1980 would result in an approximation of the magical population. So I visited Google and Wikipedia, not academically reliable sources but then again we are talking about a fictional world here.
The numbers I found most easily were a population of 48 million and a birth rate of 700 thousand. Yes, I have rounded the numbers for convenience. Now, 48,000,000 divided by 700,000 equals 68.6 people per birth. I have been estimating that there were 40 kids in Harry's year, meaning 40 magical births in 1980 so 68.6 multiplied by 40 equals an estimated population of 2,750. Now this is significantly lower than my other estimates BUT does not take into account the idea that magical people live longer than non-magical. In the first set of calculations I made, I assumed that magicals lived twice as long which would yield a population of roughly 5,500. This of course assumes that the population would follow the same standard bell curve for ages with the mean doubled.
Now the overall population of the UK in 1980 was 56 million, and if we assume a magical population of 55 hundred we see that roughly 1 in 10,000 people are born with magic. The world population in 1980 was 4.4 billion so the global magical population would be approximately 440 thousand and roughly 25% of the wizards in the world went to see the Quidditch World Cup.
Anyways, I've seen folks come at this number from several different directions and the results seem to consistently point to a magical population of Britain in the Harry Potter years to be around 4,000 to 5,000 and roughly 1 in 10,000 people being magical.
So thanks to joemjackson and hakon2feb for an amusing little diversion.