A large minority of people in the UK believe multiculturalism has undermined British culture and that migrants do not properly integrate, according to some of the broadest research into the population’s attitudes to immigration.

The study, conducted over the last two years, also reflects widespread frustration at the government’s handling of immigration, with only 15% of respondents feeling ministers have managed it competently and fairly.

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On balance, the UK population appears to be slightly more positive than negative about the impact of immigration; however, 40% of respondents agreed that having a wide variety of backgrounds has undermined British culture.

More than a quarter of people believe MPs never tell the truth about immigration and half the population wants to see a reduction in the numbers of low-skilled workers coming into Britain from the EU.

The study was based on a survey of 3,667 adults carried out in June by ICM, as well as 60 citizens’ panels carried out on behalf of the thinktank British Future and the anti-racism group Hope Not Hate.

“The lack of trust we found in the government to manage immigration is quite shocking,” said Jill Rutter, the director of strategy for British Future. “People want to have their voices heard on the choices we make, and to hold their leaders to account on their promises. While people do want the UK government to have more control over who can come to the UK, most of them are ‘balancers’ – they recognise the benefits of migration to Britain, both economically and culturally, but also voice concerns about pressures on public services and housing.”

Panel discussions regularly revealed negative views about Islam, with participants repeatedly mentioning Rotherham and Rochdale, where child sex abuse scandals were uncovered among groups of Asian men.

However, 63% of people felt migrant workers supported the economy by doing the jobs British workers did not want to, and a similar number said they brought valuable skills for the economy and public services such as the NHS. Fifty-nine percent believed that the diversity brought by immigration has enriched British culture, but half said public services were under strain from immigration and that migrants were willing to work for less, putting jobs at risk and lowering wages.

The study found that people in large cities were the most likely to be positive about immigration, with scores declining as settlements became smaller, with rural residents the least positive.

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“Immigration is a national issue, but people see it through a local lens,” said the report’s co-author Rosie Carter of Hope Not Hate. “Where people live, and their living conditions, makes a real difference – that includes the perceived impact of migration on their community, broader grievances about economic insecurity and levels of contact with migrants and ethnic minorities too.”

The report’s authors are calling for an official “national conversation” about immigration that would give people a chance to express their concerns “so anxieties are not driven underground or exploited by those seeking to stoke division”.

• The subheading of the graphic was amended on 17 September 2018 to clarify that 10 shows the most positive impact in the mean scores given.