IF integration means doing a bit better in education and the job market, then there are grounds to be optimistic about the status of Muslim communities across western Europe. But when you ask Europeans how they feel about Islam and its adherents, then the picture is much harsher and in some ways getting worse.

Those are the broad impressions left by a raft of recently published surveys on the subject. The authors of a study by Germany’s Bertelsmann Foundation, focusing mainly on Britain, France, Germany, Switzerland and Austria, found some encouraging indicators on schooling and employment but still reported a big income disparity between Muslims and non-Muslims.

Professional progress was “not accompanied by an equal level of…social acceptance,” noted the report, which looked not at refugees but longer-standing Muslim residents. The authors were troubled by the finding that 20% of respondents did not want Muslim neighbours. That number would almost certainly have been higher if the study had looked at countries further south and east. A poll by Pew Research, an American think-tank, found that a majority of people in Hungary, Italy, Poland, Greece and Spain harboured hostile attitudes to Islam while only a minority of northwestern Europeans held similar views.

The Bertelsmann report welcomed the fact that in France, only one in ten Muslims leaves school before turning 17, compared with about a third of Muslim youngsters in Germany. But learning doesn’t seem to guarantee earning. In neither Germany nor Switzerland was there much difference between the employment rate of Muslims and non-Muslims. In France, by contrast, the jobless rate was 14% for Muslims compared with 8% for non-Muslims.

Moreover, there are some clear signs of hardening attitudes. In England, around four people in ten acknowledged that they have become more suspicious of Muslims following terrorist attacks in London and Manchester. That was one of the findings of the latest study published by Hope Not Hate, an anti-extremism lobby group.

Looking at a series of recent data, it concluded that in many ways sentiment in England was gradually becoming more liberal and tolerant of diversity, but Islam and the reactions it inspired were a clear exception. About half the population apparently thought Islam posed a “threat to Western civilisation” while a quarter regarded it as a “dangerous” religion because of its perceived capacity to incite violence. The picture changes depending on how the question is framed. The pool of respondents who opined (50% versus 22%) that the Muslim faith was a civilisational threat also agreed by a clear majority that it was wrong to blame an entire religion for a few extremists.

In Germany, a widely-quoted poll last year found that more than half the population believed that Islam did not belong in their country. But attitudes to Muslim people, as opposed to their religion, can sometimes be much more emollient, albeit varying a lot with the respondent’s political ideology.

Pew found that half the Germans who hewed to the political left thought Muslims were making a good effort to adapt to the country’s way of life, compared with one in five of those who leaned rightwards. The numbers for Britons of right and left were almost exactly the same. Given the many different ways in which progress (or regress) can be measured, the state of Islam in Europe may always be a vessel that some see as half-empty and others see as half-full.

What's worrying is that almost every terrorist movement aims to polarise feelings in a way that drives people into opposing camps. The terrorist who claims to represent a certain community often hopes that the authorities, and perhaps society as whole, will stigmatise that community and provoke in it a defensive mood, so that violence starts to seem like a reasonable option. Historically, such polarising tactics have often worked.

Although things have not yet reached that point, these poll results suggest something sinister: it’s perfectly conceivable that the murderous van-drivers and knife-wielders who claim to speak for Muslims in Europe could enjoy a similar “success” in polarising sentiment across the continent.