More than a third of people in the UK believe that Islam is a threat to the British way of life, according to a report by the anti-fascist group Hope not Hate.

The organisation’s annual “State of Hate” report, which will be launched on Monday, argues that anti-Muslim prejudice has replaced immigration as the key driver of the growth of the far right.

In polling conducted by the group in July last year, 35% of people thought Islam was generally a threat to the British way of life, compared with 30% who thought it was compatible. Forty-nine per cent of those who voted Conservative in the 2017 general election thought it was generally incompatible, and 22% of Labour voters agreed.

Nearly a third (32%) said they thought there were “no-go areas” in Britain where sharia law dominated and non-Muslims could not enter. Almost half of Conservative voters (47%) and those who voted to leave the EU (49%) believed this was true.

The report said that while polling showed that attitudes towards Muslims in Britain had improved between 2011 and 2016, the terror attacks in the UK in 2017 had had a negative impact on perceptions.

In a separate poll of more than 5,000 people in August 2018, 30% said they would support a campaign set up by local residents to stop proposals to build a mosque near where they live. Twenty-one per cent say they would still support the campaign if either side became violent, because the matter was so serious.

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Among the issues in the report is that of leftwing antisemitism. Hope not Hate said that while extreme antisemitism and Holocaust denial were less common, there were many examples of “conspiratorial” antisemitism and the use of antisemitic tropes, “especially in relation to supposed Jewish power”.

The report points to research that found an increase in antisemitic Google searches in the UK. It found that 5% of UK adults did not believe the Holocaust happened and 8% said the scale of the Holocaust had been exaggerated.

The report’s authors said a large group was involved in “denying a problem exists and dismissing the issue as a rightwing and Zionist smear”. It concluded that the Labour party was still not doing enough to tackle antisemitism.

“The family history of so many members of the British Jewish community includes first-hand experience of persecution. Many people in the Jewish community therefore identify with a sense of the precariousness of their safety, where material security and educational attainment are not seen as guarantors of security and safety,” it said.

“The inability of the Labour party leadership to understand and acknowledge this experience is particularly chilling when the Labour party and the left in general hold values of equality and antiracism as core to their identity.”

The report also found that while the numbers arrested for terror-related offences in 2018 was down on the previous year, there was a growing threat of far-right terrorism, which came both from organised groups such as National Action and from lone actors who are radicalised over the internet.

The group warned that there could also be a rise in support for Islamist extremist group Al-Muhajiroun following the release of one of its founders, Anjem Choudary, from prison.

“Our latest polling also reveals a disturbing level of anti-Muslim prejudice and discourse running through society, with a third of people saying they believe there are Muslim-run no-go zones, and rising antisemitism on the left, which we have exposed in a new investigation,” said Nick Lowles, the chief executive of Hope not Hate.

“Meanwhile, while the banned terror group National Action has finally been destroyed by the authorities, there is a growing threat of violence from the younger neo-Nazis emerging in their wake. There are justified concerns that the police response to these rising threats, especially against MPs, has fallen short. We believe a very real threat remains from terrorism carried out by lone actors, too, radicalised over the internet.

“Added to this febrile mix is the release of Anjem Choudary and many of his network’s leading figures, likely to regalvanise their supporters and provide yet another seedbed for the far right to grow their support, too. We cannot wait for a traditional, united, far-right umbrella organisation to emerge before we act. We need to start connecting the dots now.”