Last week four British Muslims told the BBC’s Panorama why they believe the government is right to identify “non-violent extremism” as the ideology that helps lays the ground for violent extremism. They explained that this non-violent ideology is the politicised version of puritanical Sunni Islam that dominates Saudi Arabia and which has been exported to Britain and around the world over decades.

The programme showed how Salafi Wahhabism is wreathed in anti-westernism, contempt for parliamentary democracy, reactionary attitudes to gender equality and gay rights, and disdain for other faiths. Through its UK-based adherents, this puritanical strain of Islam has taken on a life of its own here with a proliferation of Islamic teaching institutions, activist groups and Islamic satellite channels. It “takes young Muslims to the front door of violent extremists” said Sara Khan.

Khan runs a counter-extremism organisation called Inspire. Like the three other interviewees, she believes Salafi Wahhabism is growing and “drowning out the prospect of developing a British version of Islam”.

Adam Deen runs an institute promoting “critical thinking and rational thought” among British Muslims. He told Panorama that puritanical Islam is “a cancer. We have to pinpoint where the problem is.” It is rare and brave for British Muslims to speak with such candour. They know how hard it is for many ordinary Muslims, let alone extremists, to accept that Islamic theology is prone to being turned into bad theology when it morphs into a toxic political ideology.

Barely had transmission begun when Deen’s twitter account was hit by a stream of abuse. He was a “coconut aren’t you lad?” (brown outside, white inside); a “scumbag white man”; a “white liberal man”; a “kafir lover” (a derogatory Arabic term for “infidel” or “disbeliever”); he had been paid by David Cameron to “become a complete donkey for the Home Office, Kafir lover”; he was a “Kafir apostate” (a Muslim who had abandoned Islam) who should go to Saudi to be “executed”; a “little snake”; “quite frankly mate, get lost” – and so on.

Likewise Khan was dismissed as a “feminist” who was “parroting the same rhetoric” as another interviewee Manwar Ali. An ex-Afghan jihadi who has long since renounced violence, Ali explained that dividing the world starkly into “them” and “us” (believers and non-believers) was the first step on the road to violent extremism. Today, Ali counsels Muslims on how to contain anger. “We are quick to judge, quick to condemn, quick to be offended, quick to dismiss. Everybody is shouting” he says.

Last autumn, Khan led a campaign by Muslim women against the “barbarism of Islamic State” promoted by The Sun newspaper’s front page featuring a woman wearing a Union Jack hijab. This provoked a mouthy young Islamist called Dilly Hussain to describe Khan as “the government-friendly desperado”. He is deputy editor of a new website called 5Pillars which refers favourably to the extremist organisation Hizb-ut-Tharir as “working for the re-establishment of the Caliphate”.

While Hussain sermonises about “Islam’s true teachings of brotherhood” he also does a particularly venomous line in abuse against the “sisterhood”, describing Khan as an “airhead” who belongs to an “ultra-minority of secular liberal ‘Muslims’ who service nothing and no one but Islamophobes.” He has likewise called another female Muslim critic a “stupid liberal cow”, a “fat cow” and a “p***head” who writes “drunken liberal garbage” and should “do one”.

The personal vituperation and constant smearing by Muslims of co-religionists who dare to challenge this kind of non-violent extremist narrative helps explain why more have not put their heads above the parapet. “It’s not my arguments they attack, but the way I dress,” says Khan. “It’s because I don’t wear a headscarf or the fact that I’m not ‘a proper Muslim’ even though I am actually a practising Muslim.”

The reaction to Panorama highlights the challenge in countering the extremist narrative. As MI5’s former head Baroness Manningham-Buller emphasised last week, ultimately the lead will have to come from Muslims – not the government.

Dilwar Hussain (no relation to Dilly) runs an organisation seeking to reform Muslim thought and practice. He says that while the non-violent extremists divide the world into Muslims and non-Muslims, the real “Them” and “Us” faultline lies “much more within the different factions of Islam. There are tough times ahead.”

The influential Saudi-trained imam Dr Haitham al-Haddad fits the government’s definition of a non-violent extremist. He has set up, or advised, a multitude of Islamic organisations here, and is a judge at the Sharia Council in east London.

Haddad regards music as a “prohibited and fake message of love and peace” and gender equality as a “very evil thing”. He has advised Muslims not to “integrate… simple as that”. He makes no bones about exploiting “filthy” man-made parliamentary democracy to try to return a Muslim majority government in “50 years, something like this” as a prelude to “Islam spreading all over the world” under “the law of Allah” which is “superior to any other law”. Once achieved this would be enforced by offensive jihad, although Haddad prefers to call it merely “pro-active” jihad. He also believes Muslims in an Islamic state who renounce their faith should be executed and adulterers stoned.

Ali, Khan, Deen and Dilwar Hussain all agree that ultimately the only way to counter this kind of bigotry and intolerance is to forge a new and recognisably British interpretation of Islam. “We don’t want Islam to be seen in this country as a foreign immigrant, exotic phenomenon,” says Hussain. “We want it to be about openness, as opposed to rigidity and closedness. We want it to be naturalised, and normalised in this country.”

A British version of Islam that embraces British culture, rather than seeking to eradicate it, will need to dispel the perception among Muslims that western foreign policy is the root cause of violent extremism. This is “dishonest and dangerous” says Deen. The fact that Islamist terrorism pre-dates Iraq and Afghanistan and that there are many millions of non-Muslims just as aggrieved at foreign policy who do not resort to violence, points to toxic theology as the real culprit.

Forging a British Islam will also require reversing an apparent trend towards more segregated Muslim communities in places such as Birmingham, London and northern mill towns. This is the decades-long consequence of a weakening collective identity, once celebrated as “multiculturalism”, now lamented as sleepwalking our way into segregation.

Although some recent surveys have found that Muslims identify more strongly with Britain and its democratic institutions than the general public, they may mask some uncomfortable truths. “We need to drill down into what that actually means,” says Dilwar Hussain. Might respect for democracy actually mean gratitude for the hands-off multicultural tolerance that encouraged a very conservative version of Islam or marriage with your first cousin? “We’ve avoided these sort of questions in the past because they are all too difficult.”

Other surveys show that overall residential diversity in Britain is growing but, again, this brighter picture may not be matched by the reality on the ground. The Social Integration Commission has found poor social integration in some highly diverse areas, suggesting that residential integration doesn’t necessarily translate to meaningful social interaction. In other words, silent toleration won’t provide the glue for true cohesion. “When we talk about ‘We’, Muslims mustn’t just mean ‘We Muslims’” says Dilwar Hussain. “They must mean ‘We’ as in everyone – our neighbours.”

This helps explain why the Home Office has struggled to find any evidence that government integration initiatives have had any significant impact. Core British, or Western values seem to be drifting beyond a growing number of Muslims.

Hussain, Khan, Ali and Deen have put their heads above the parapet in the hope of stimulating a wider acknowledgement among Muslims that there is a problem within Islam, however much political leaders assure us – with the best of intentions – that terrorism is either “nothing to do with Islam” or a “distortion of Islam”. It cannot be both. The reality is there are many Islams.

These four British Muslims have lost their fear of confronting their extremist co-religionists who claim their interpretation of Islam is mainstream Islam. “I’m not afraid to confront this mafia now,” says Deen. “Before I had a fear that I would be ostracised from the community – it was an unspoken rule that you don’t have a different opinion because you will be shut down. It’s a bully force.

“But I know now that my position is cogent. I know that irrationality will not stand in the way of rationality.”

There is still no army of foot soldiers like Deen, Hussain, Khan and Ali who are as well organised, funded or vociferous as their regressive co-religionists. They do, though, mark the battleline over what will be a generation-long struggle for a British Islam. For all the abuse heaped on them for speaking out, they offer the only credible answer to forces within this country that threaten to divide us in the most dangerous way imaginable.