Should government be picking winners within Muslim communities in order to combat the threat of violent jihadism? And does it work - any more than the corporatist strategy of picking winners among big enterprises succeeded in the 1970s?

This approach is a key strand of the Government's new national security strategy, launched last week. The flagship programme for delivering it is the Preventing Violent Extremism Pathfinder Fund (PVE), amounting to £45 million over three years. It was created after the 7/7 bombings, reflecting Tony Blair's belief that the Muslim Council of Britain had not done enough to fight the extremists.

Blair and Ruth Kelly, the Secretary of State for Communities and Local Government, contended that local authorities, police and communities were best positioned to identify those grassroots Muslim groups who could challenge advocates of violent Islamism.

But key local authorities are now in revolt. According to the Local Government Chronicle, many councils are refusing to adopt a target to “build resilience to violent extremism” for fear of damaging community relations. Their Muslim constituents are said not to like PVE because they think the programme stigmatises them. And non-Muslims are said to resent the fact that Muslim groups seem to be benefiting.

A more serious point is whether local government is able to choose appropriate Muslim partners. Yes, municipalities enjoy on-the-ground expertise. But what kind of grassroots expertise? Can they really discriminate between different varieties of Islamism? If even MI5 finds difficulty drawing the line, what hope for aldermanic worthies?

Earlier this year Paul Goodman, the Shadow Communities Minister, pressed Ms Kelly's successor, Hazel Blears, to confirm that money was not falling into the hands of extremists. Blears could not supply that reassurance, though she is the least blameworthy figure in all this. More than any other Cabinet minister, she “gets” radical Islamism. But it is infernally difficult, even for her, to monitor which groups are worthy recipients and which aren't.

It was symptomatic that it took her department six months to answer Goodman's previous inquiries on where the funds were going. And even if they are not going to unworthy causes, are these schemes effective?

The list of grant recipients is strange. Even Conservative councils are not very rigorous in choosing partners. For example the Channel 4 Dispatches programme exposed hate preaching at the Green Lane mosque in Birmingham. A preacher, Abu Usama, urged that homosexuals be thrown from mountains. Yet the Green Lane mosque is one of the partnership organisations approved by Birmingham City Council.

Indeed, the Green Lane mosque is also a well-established interlocutor of the West Midlands Police. West Midlands Police still aver that men such as Abu Usama enjoy the “street cred” to stop radicalised young Muslim men from tipping over into violent jihadism.

Kensington & Chelsea Council has turned to the Muslim Cultural Heritage Centre to deliver a “parental empowerment programme” that aims “to foster modern, inclusive and Islamically sound relationships between parents and children. Parenting techniques are imparted and discussed from an Islamic and wider social perspective by a trained Muslim NHS psychotherapist.”

Why is it the duty of a council to “foster Islamically sound relationships between parents and children”? Who defines what is “Islamically sound”? How does picking a Muslim psychotherapist - apparently on sectarian grounds - help to prevent violent extremism?

Likewise, Westminster City Council relies on the Muslim Cultural Heritage Centre (which is not even in the city) to organise a “young people's leadership and debate programme” on foreign policy.

Why should Tory councils turn to them, of all people? The centre's name appeared in a statement on the website of Hizb-ut-Tahrir asserting that “the Muslim community in Britain has unequivocally denounced acts of terrorism. However, the right of people anywhere in the world to resist invasion and occupation is legitimate”. The statement also denounced the proscription of Hizb-ut-Tahrir - a key objective of David Cameron.

Such partnerships are reflective of the greatest weakness in PVE - and of much the Government's “contest” strategy for combating terrorism. As its name suggests, it is largely about countering violent extremism. It isn't necessarily about countering non-violent extremism.

The interplay between violent and non-violent radicalisation lay at the heart of Mr Cameron's remarkable recent address to the Community Security Trust. Cameron believes that it is not enough simply to be against jihadism on these shores. He is deeply disturbed by the sectarianism of groups such as the Muslim Brotherhood and associates such as the Cordoba Foundation - which receive PVE funds.

It's as if the Government responded to a violent insurgency from the neo-Nazi terrorists of Combat 18 by turning to Nick Griffin of the BNP, on the ground that he enjoys nationalist “cred” with alienated skinheads. After all, Mr Griffin is non-violent and believes that whites should participate in the political process. Perhaps he might stop bombs from going off. But what price would he exact for it - and what kind of society would we then be living in?

Dean Godson is research director of the Policy Exchange think-tank

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