According to the latest "Ipsos Perils of Perception" survey carried out in forty countries, most countries hugely overestimate the proportion of Muslims in their population. In Britain, for instance, people think that 1 in 6 Britons are Muslim (in fact, it is fewer than 1 in 20), that 15% of the population are Muslim (instead of the 4.8%). In addition, Britons believe that the Muslim population is growing to a much greater extent than it actually is: 22% by the year 2020 (they will probably make around 6%).
Great Britain, however, is far from being the most extreme example as it is the third most accurate country in Ipsos's so-called "Index of Ignorance". Most of the countries are much more wrong. In France, the average guess is that 31% of the population is Muslim (it is 7.5%), Canada and the United States guess 17% (it is 3.2% and 1%).
The level of growth over the next few years is highly overestimated, too. In France, people tend to think that 40% of the population will be Muslim by 2020 (the projection is 8.3%). The United States has an average guess of 23% (the projection is 1.1%) (via).
The German city of Hamburg carried out a similar survey in 2014 and came to the conclusion that only 8% of its inhabitants were close to reality when guessing the proportion of the Muslim population (via).
Photographs (mostly?) by Eve Arnold (The Nation of Islam, 1961) via and via and via and via and via