The letter to 1,100 Muslim leaders from Eric Pickles was just the kind of warm embrace one might expect from the Secretary of State charged with promoting community cohesion:

"Assalamu Alaikum" his letter began, the "great faith" of Islam had been "hijacked" by terrorists who were "an affront to Islam". He said that he was "proud" of how British Muslims had spoken out against the slaughter in Paris. "British values" were "Muslim values". "Islam and its message of peace and unity" made Britain "a better and stronger place". Pickles also urged Muslims to report any instances of hatred.

And the reaction from the organisation that says it speaks for British Muslims?

"The letter has all the hallmarks of very poor judgement which feeds into an Islamophobic narrative" complained Talha Ahmad, a spokesman for the Muslim Council of Britain. How so? Because within the Pickles bear-like hug, was also this request to imams: "You have a precious opportunity, and an important responsibility: in explaining and demonstrating how faith in Islam can be part of British identity."

There was a need to explain more clearly than ever "what being a British Muslim means today: proud of your faith and proud of your country."

Children were warned not to listen to others because they 'are all liars'

Why? To ensure that "Islam's true message of peace triumphs over those who seek to divide our communities."

The MCB snapped back by suggesting Pickles was parroting the "far right" for suggesting that "Muslims and Islam are inherently apart from British society."

Really? Pickles had also lambasted the "vitriol espoused by the thugs of the English Defence League and Britain First" as being "just as much an affront to British values as the teachings of the preachers of hate."

So far so wearily predictable. The MCB's reaction reflects its traditionally defensive response to any attempt to engage in a candid debate about the relationship between extremism and integration. Where Pickles's letter is polite and beseeching, the MCB come over as self-righteous and borderline rude.

We seem to have tiptoed round this debate for ever. At nearly 3m, Muslims now represent five per cent of the population, projected to rise to 5.5m or 8.2 per cent by 2030.

Yet there appears to be a high degree of separation in some towns and cities with Muslims and non-Muslims not socially interacting in a way that provides the essential glue for a cohesive common life.

Ultimately, it is meaningful integration that will provide the resilience to toxic theology.

Beyond the 600 (and rising) British Jihadists who have joined Islamic State in order to find meaning in their lives, the Home Office now assesses that there are tens of thousands of British Muslims who do not subscribe to core British values of tolerance, freedom of worship, democracy, the rule of law, parliamentary democracy and equal rights regardless of race, gender or sexuality.

"These values are no longer self-evident," a home office official told me.

Ministers and officials have come to the view that, although violent extremists represent only a fringe, they do share a much broader spectrum of belief that stretches deeper into Muslim society than the MCB has cared to admit.

Broadly, this spectrum divides humanity into a bipolar world of "Them and Us" - believers and nonbelievers. At this spectrum's most violent fringe, there is the satanic figure of "Jihadi John" the south London cut-throat whose catastrophic lack of empathy for "Them" allows him to saw through the necks of his fellow British citizens and others from around the world just as casually as a butcher saws through a leg of lamb.

At the other end of this spectrum are Islamists who are not violent and are horrified by Jihadi John but do nonetheless partly share the extremists' hostility to the West and to liberal values. There is a sniffy "righteousness" about Islam over western living, as one Muslim academic put it to me.

We saw this with the secretly taped thoughts of a Muslim governor at one of 16 Birmingham state schools where governors and teachers had tried to inculcate a "Them and Us" mind-set into Muslim children. "I tell you, our women are much, much better consciously in the heart than any white women" he said. "White women have the least amount of morals."

Two official inquiries into the so-called "Trojan Horse" plot found evidence of Muslim children being warned not to listen to Christians because they were "all liars", how they were "lucky to be Muslims and not ignorant like Christians or Jews", of children being warned they would go to hell if they didn't pray, of segregation, of homophobia, a hard-line curriculum, contempt for the armed forces and even scepticism about the murders of Drummer Rigby and American civilians killed by the Boston nail bombers.

The Home Secretary says that there is "undoubtedly" a thread that "binds" this kind of non-violent "intolerance hatred and a sense of superiority over others" to "those who want to impose their values through violence." After a decade of what Cameron describes as "passive tolerance" which "stands neutral between different values", he says it is time to "confront" non-violent extremism by asserting "a lot less passive tolerance" and a lot more "active, muscular liberalism."

The MCB certainly appears to regard these sentiments as problematic. It has described the government's definition of extremism as "ambiguous."

Here is the definition: "Vocal or active opposition to fundamental British values, including democracy, the rule of law, individual liberty and mutual respect and tolerance of different faiths and beliefs."

The MCB also says this definition is "inconsistent" with the government "upholding… regimes that have subverted democracy" – a reference, presumably, to the government's recognition of President Abdel Fattah el-Sisi as head of a government democratically elected after overthrowing the Muslim Brotherhood government. But then almost every other major country in the world has "upheld" the Sisi government including the UN and EU.

The MCB also disputes that most of what was found in Birmingham was not evidence of "extremism" but merely of "conservative Muslim practices." Are homophobia, intolerance of other faiths and anti-Jewish attitudes just "conservative" Muslim practices? Surely bigotry is a fairer description.

When it comes to British values, the MCB is itself ambiguous. On Monday, the MCB Secretary General Shuja Shafi assured the Prime Minister that "British values are indeed Islamic values."

Yet, in an email to me last November, the MCB dismissed British values as "nebulous."

I was preparing a BBC Panorama programme on extremism, which was transmitted last week. It highlighted a number of clerics who, while not promoting violence in the UK, said that Christians were "usually liars", that gender equality was "evil", parliamentary democracy "filthy" and who supported the death penalty for apostates - Muslims who abandon Islam.

Sara Khan, a practicing Muslim who runs a counter-extremism organisation, was one of four Muslims who told Panorama that they agree with the government that non-violent views like this undoubtedly do open the door to violent extremists.

I wanted to ask the MCB if it agreed, or whether, as in Birmingham, they thought such views were just a reflection of "conservative Muslim" beliefs.

They declined to be interviewed on the grounds that I - like Eric Pickles - was helping to feed "the far-right."

For all the MCB's sincere condemnation of extremist violence, its confusing and contradictory positions suggest it has yet to find the courage and the confidence to lead the fight against extremism.

As Sara Khan says: "I have not to date seen any grassroots counter-extremism strategy from the MCB."