PARIS (RNS) When Americans demonstrated against President Trump’s recent entry ban against citizens of seven mostly Muslim countries, marchers in London, Paris, Berlin and other European cities quickly joined in the protest. The message from across the Atlantic seemed to be “we’re with you.”

The televised reports of the protests told only half the story, however. In fact, even less than half.

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According to two extensive recent opinion polls, majorities across Europe are deeply concerned about Muslim immigration and support an immediate end to it, even as Europeans vastly overestimate the actual Muslim populations of their countries.

Voters in several countries back a complete immigration ban at levels notably higher than those in the United States. Anti-immigration politicians in Poland, Hungary and elsewhere are gaining ground in Western Europe.

A survey released last week by the British think tank Chatham House said the impression that Europeans oppose an immigration ban — bolstered by widely reported critical comments from German Chancellor Angela Merkel or London Mayor Sadiq Khan — did not reflect the overall reality.

“Our results are striking and sobering,” a press release read. “They suggest that opposition to any further migration from predominantly Muslim states is by no means confined to Trump’s electorate in the U.S. but is fairly widespread.”

Amsterdam’s daily de Volkskrant, one of the few European newspapers that reported on the survey, pointed out the gap between image and reality.

“Europeans are not at all that negative towards the American president’s ideas,” the release said. “In fact, a majority of Europeans are for an immediate stop to immigration.”

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The survey of more than 10,000 people in 10 European countries showed that 55 percent of all respondents agreed that all further migration from mainly Muslim countries should stop, 20 percent disagreed and 25 percent neither agreed nor disagreed.

According to a CNN poll, 47 percent of Americans supported Trump’s ban. Another poll, by Ipsos, put this support at 49 percent.

“Majorities in all but two of the 10 states agreed (on an immigration stop), ranging from 71 percent in Poland, 65 percent in Austria, 53 percent in Germany and 51 percent in Italy,” Chatham House said in its report. Support for a ban fell below half only in Britain (47 percent) and Spain (41 percent).

Except for Poland, the study noted, the countries most opposed to more immigration have either been on the front line of the migrant crisis or suffered terrorist attacks on their soil in recent years.

Of the countries with over 60 percent support for a ban, Austria and Hungary were flooded by the human wave that passed through southeastern Europe on its way to Germany in 2015. France and Belgium have seen deadly attacks by Islamist radicals — some of whom came with the refugees — carried out on their own soil.

“It is also worth noting that in most of these states the radical right is, to varying degrees, entrenched as a political force and is looking to mobilize this angst over Islam into the ballot box, either at elections in 2017 or longer term,” the report said.

Support for stopping immigration isn’t restricted to the far right, the study pointed out. The Netherlands, France and Germany face elections this year, and their once-shunned far-right parties are expecting to make important gains.

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“There is also some evidence that public opposition crosses political boundaries, with three-quarters of those who self-classify themselves as on the right of the political spectrum and more than a third of those on the left supporting a halt,” it said.

Another major survey, released by the Paris-based Ipsos polling institute just before Christmas, hinted at one strong reason why concern may be so widespread. In every European country polled, voters think the Muslim populations in their countries are much higher than they really are. The gap between fact and fear can be enormous.

In France, home to Europe’s largest Muslim minority, voters estimated 31 percent of the population belonged to the Islamic faith. In reality, only 7.5 percent do. In Italy, they account for 3.7 percent of the population, but voters there guessed their proportion at 20 percent.

Germany, Belgium, Sweden and the Netherlands showed equally high overestimates.

Even countries with almost no Muslims got their guesstimates wrong. Poland and Hungary both have less than 0.1 percent Muslims in their populations, but their voters guessed they had 7 percent and 6 percent respectively.

North American readers shouldn’t think this is a particularly European myopia. According to Ipsos, the U.S. population is 1 percent Muslim, but respondents there estimated it at 17 percent. Canadians also guessed their Muslim population at 17 percent, while the actual figure there is 3.2 percent.

The Ipsos poll showed Europeans also vastly overestimated future growth of their Muslim populations, with all of them expecting rapid rises in their numbers in the next few years.

“Does Europe fear Muslims more than the United States?” asked John Lloyd, a contributing editor to London’s Financial Times, in an analysis.

“The more urgent question is whether those who support a ban on travel and immigration from Muslim-majority countries will lead nationalist parties to victory,” he said.

“To describe the new far-right parties in Europe as 'populist’ is to categorize them as outside the pale of mainstream, liberal politics: to admit that they are popular is harder.

“But they – or at least their policies – are. The dark night of fascism has not fallen on America, nor on Europe, and isn’t likely to, but fear and rejection of immigration haunts both. In 2017 Europe will show, in the Dutch, French and German elections, how dark the night can be.”

(Tom Heneghan is a correspondent based in Paris)