Communities across the UK have told Britain’s first counter-extremism commissioner that they are increasingly facing “a climate of intolerance and polarisation”.

Speaking several months into a nationwide investigation to quantify the scale and reach of extremism, Sara Khan said she had been shocked by the depth of disquiet expressed to her by the residents of the 13 towns and cities she has so far visited.

Khan, appointed by Theresa May in the wake of the Manchester Arena attack, told the Observer: “I was really shocked that in every place I visited I heard deep concerns about the activity and impact of the far right.

“Councils across the country raised the impact the far-right demonstrations have on whole towns, exploiting tensions and stoking division. I repeatedly heard about a climate of intolerance and polarisation.”

Khan has visited Middlesbrough, Manchester, Cardiff, Portsmouth, Birmingham, Luton and London among others, along with interviews from 400 experts, activists and civil society groups that together with a public consultation will help form a study to be published next spring.

One youth worker from the south of England told Khan of his fears that a “whole generation of vulnerable children” could be lost to the far right. Elsewhere, a local education group said it had seen increasing numbers of children making racist and extremist statements in schools.

Khan’s appointment in January was criticised by some who claim she is too close to the government. But Khan said her investigations had detected a sense Britain was on the cusp of a fresh wave of rightwing extremism: “This backs up what experts have been telling me – that we are seeing a new wave of the far right: modernised, professionalised and growing; supported by a frightening amount of legal online extremist material.”

Matthew Feldman, director of the centre for fascist, anti-fascist and post-fascist studies at Teesside University, said he was not surprised by Khan’s initial findings: “I think this is the most propitious time for the radical right since the end of the second world war, that hasn’t yet translated into activists, members or a party that might be able to overcome the first-past-the-post system.”

Khan’s comments come days after the country’s most senior counter-terrorism officer, the Metropolitan police’s Neil Basu, told the home affairs select committee that far-right extremists and Islamists were “feeding each other” and that police were currently presiding over 700 live terrorism investigations. Basu’s predecesscor, Mark Rowley, said in August that the UK had not “woken up” to the threat posed by the far right.

Rowley warned the public and politicians not to underestimate the situation, describing how National Action, a proscribed neo-Nazi organisation, has “a strategy for a terrorist group” with online information on how to create discord in communities and evade police surveillance.

Home Office data shows that white people now constitute the largest proportion of arrested terrorism suspects for the first time in 13 years. Meanwhile, the number of people referred to the government’s counter-extremism programme, Prevent, because of concerns over rightwing extremism has grown by more than a quarter.

Khan added: “Youth workers in the south feared vulnerable young people could easily be sucked into a world of hatred. In the north, refugees and those from a minority background spoke of their fear of leaving their home during far-right marches.”

Khan also warned that the ideology of radical Islam was still proving seductive to some British youngsters. “In one city I heard concerns that we are losing many young Muslims to the toxic online narratives of Islamist extremists,” she said.