One in six Britons believe the growth of the Muslim population “poses a foundational threat to UK culture”, with hostile attitudes towards Muslims at risk of being normalised, a study has found.

The study by the social integration thinktank British Future and the British Muslim Trust – the government’s official partner in monitoring Islamophobia – found that most Muslims (73%) think the UK is a good place to be Muslim, and that a majority of Britons believe Muslims are as British as white non-Muslims.

However, 17% of the wider public “strongly agree” that “the growth in the Muslim population poses a foundational threat to UK culture”, while 19% do not agree that “Muslims born in this country are as British as white, non-Muslim people born here.”

The British Muslim Trust launched in July last year, starting a helpline for anti-Muslim hate crimes and meeting people across the country.

Its director, Akeela Ahmed, said that “time and again”, Muslims were saying they felt “their place and identity” was being questioned and scrutinised in ways it hadn’t been before, when they had integrated and worked and studied hard.

Ahmed warned in the report that while British Muslims continue to express “a deep sense of belonging to this country”, if the next generation grows up doubting that this is their home, “it will have unintended consequences on social cohesion.”

She added: “Two threads run through this evidence. The online world is plainly shaping attitudes, carrying misinformation and hostility further and faster than ever before.

“Too many people simply do not know a Muslim – the interpersonal contact and connection that builds trust is missing from their daily lives. Both must be addressed … It is in those local relationships, more than anywhere else, that prejudice is undone.”

The survey of attitudes drew on a representative sample of 2,000 people to inform the report, Understanding Anti-Muslim Hostility: Foundations for Action, which examines social attitudes rather than making detailed policy recommendations.

The research found 52% of the public said they believed Muslims were as British as white people who are not Muslim, while 57%, agreed that “it is possible for Muslims and non-Muslims to live well together in towns and cities around the UK.”

The survey found that a majority of British Muslims (61%) – of whom about 1,000 were surveyed – felt less safe after the first Unite the Kingdom rally was held in September last year, rising to 69% of Muslim women.

Nonetheless, the research found confidence in Muslims’ sense of British identity – with 69% of Muslims agreeing that British-born Muslims are “as British as white, non-Muslim people born here”.

Meanwhile, a majority of the public (63%) recognise that there is prejudice against Muslims, and 61% support government action against anti-Muslim prejudice, including the most supportive 20% of people who feel the government should take strong action. Another group (41%) said government action is important, provided there are balances to protect freedom of speech. Only 7% were opposed to action on the issue.

More than half of Muslims (56%) experienced prejudice based on their religion in the last year, which Ahmed described as “utterly intolerable”. But she said it was “heartening” that the majority of people supported action on anti-Muslim hatred.

Researchers said they found a “strong correlation” between the regularity of interaction with Muslims and respondents’ levels of acceptance towards Muslim people.

An age gap in attitudes was also identified, with 29% of over-65s seeing the contribution of Muslims as negative, but only 16% of 18-24s.

Sunder Katwala, the director of British Future, said: “It’s deeply worrying that one in six people hold sweeping, hostile prejudices towards Muslims in Britain. Most people do not agree with them – but if this trend continues unchecked, there is a real risk that these attitudes become normalised in wider society.

“It cannot be OK for a section of our society to be subjected to such hostility because of their religion. This shouldn’t be a matter for polarised political debate but a basic norm that we can all agree on. We must protect free speech and we must also protect our fellow citizens from hatred.”