Data was collected on hundreds of thousands of men from 15 European countries.
For British men, the average height at age 21 rose from 167.05cm (5ft 5in) in 1871-75 to 177.37cm (5ft 10in) in 1971-75.
A public health expert said height was a “useful barometer” but it was crucial to focus on improving health overall.
The paper, published in the journal Oxford Economic Papers, looked at data from sources including military records and modern population surveys from the 1870s to 1980 in 15 European countries.
It looked only at male height because there was too little historical data for women.
Genes may be commonly seen as the main determinant of height, but although they explain the difference between individuals, they would not explain the trend seen in this paper, its lead author said.
Prof Tim Hatton of the University of Essex said there was no “Darwinian explanation” to the trend. “People are surviving in the 20th Century who would not have survived in the 19th,” he added.
The researchers said the gene pool “cannot account for substantial increases in mean stature over four or five generations”.
Growth is significantly affected by what happens in the first two years of life, they said.
So, a high rate of illnesses such as respiratory diseases or diarrhoeas – which caused many infant deaths – would also affect survivors’ development and therefore their subsequent height.
Infant mortality rates fell significantly throughout the period studied.
Another factor taken into account by the researchers was an increasing move to smaller families – meaning fewer people to feed.
Higher income, more sanitary living conditions and better education about health and nutrition could also have had an effect, they said.
The paper also shows that height patterns varied across different countries.
Contrary to what might have been expected, in northern Europe – including in Britain – there was a significant surge in average height in the period covering the two world wars and the Great Depression, before the introduction of the national health service.
Increasing height is a reflection of how the availability of food and nutrition had broadly improved until the recent excesses of fat and sugar”
Dr John MiddletonFaculty of Public Health
Prof Hatton suggested this was because the benefits of long-term improvements in sanitation, hygiene and nutrition were being seen.
During periods of war, he explained, more women were earning an income and rationing actually improved diets for some.
However, in southern Europe there was a sharp acceleration in average height seen after World War II.
This was when those countries saw significant income growth and adopted some of the social measures that northern European countries had adopted more slowly in previous decades, Prof Hatton said.
He added: “Increases in human stature are a key indicator of improvements in the average health of populations.”
Dr John Middleton of the UK’s Faculty of Public Health said: “Does how tall we are really tell us how healthy we are? This interesting research suggests that it’s certainly a factor.
“Increasing height is a reflection of how the availability of food and nutrition had broadly improved until the recent excesses of fat and sugar.
“However, we can’t conclude that shorter men are somehow unhealthier. Like a lot of research, this paper prompts more questions than it set out to answer.
“While our average height is a useful barometer to bear in mind, what we really need is to tackle the many reasons for poor health that we can address.
“Employment is one of the best ways to do that, which is why we need to focus on more than just diet and exercise when it comes to improving the nation’s health.”