Jacqui Smith's announcement yesterday of tougher measures to exclude "preachers of hate" is the latest in a series of initiatives to prevent young British Muslims turning to violent extremism. A mushrooming array of guidelines for schools, colleges and councils emphasises the need to challenge the narrative al-Qaida uses to attract recruits.

These guidelines do nothing to challenge the dominant narrative by which violent extremism is commonly explained, a narrative that sees even peaceful groups as transmission belts on which insecure Muslims are shuffled towards violence. However, there is a very different narrative of British Islam, which the government is less keen to talk about. There is a reason for that.

The dominant story is of a second generation who grew up in the Paki-bashing 80s and suffered a profound identity crisis on reaching adulthood. Torn between the culturally based Islam of their families and the pressures of contemporary society, these Muslims proved easy prey for radicalisation by exiled clerics from hardline groups, who presented a narrative of historical oppression going back to the Crusades.

With variants, that model is put forward by rightwing thinktanks, Conservative ideologues, former Hizb ut-Tahrir activists and erstwhile leftwingers. At its core is the idea that even non-violent organisations such as the Muslim Council of Britain and those connected with groups like the Egyptian Muslim Brotherhood are on what the former left commentator Nick Cohen calls "a continuum whose terminus is pathological hatred". Or, as Newsnight's Richard Watson puts it: "Today's suicide bombers are yesterday's Islamists."

That narrative is powerfully countered in Race & Class, the journal of the Institute of Race Relations (on whose board I sit). Arun Kundnani's article starts from the identity crisis of second-generation Muslims - but takes it in a very different direction.

He explains the influence of the Muslim Brotherhood ideologue Sayyid Qutb, not in terms of his (undoubted) social fundamentalism, but of his insistence that it's up to individual Muslims how to interpret their religion. Echoing the Protestant reformation, Qutb advocated a global Islam, liberated from national forms. His vision gives Muslims an attachment to a world community; it is compatible with many aspects of modernity; and, on a personal level, it gives Muslims an Islamic excuse not to marry their cousins.

For some, this blend of globalism and individualism explains the attraction of political Islam to the 7/7 bombers. But it also explains the trajectory of other Muslims, who have moved from youthful militancy towards a very different kind of engagement, a trajectory of which involvement in the anti-Iraq war movement is an obvious example.

For Cohen, the Stop the War Coalition is an unholy alliance of a demoralised, morally relativist left and an "Islamist far right". If that were true, you would expect the left to sell out to Islamism on issues such as women's and gay rights, free speech and antisemitism, while the Islamists remained ideologically steadfast. In fact, far from dragging duped progressives towards a hardline Islamist agenda, much of the intellectual movement has been the other way.

So, as Catholics picketed parliament for the right to discriminate against gay couples, the MCB issued a statement supporting the legislation on the grounds that, despite Islam's opposition to homosexuality, it "stands opposed to discrimination in all its forms". Rightly, and not before time, the MCB has lifted its boycott of Holocaust Day. In a Guardian article last year, the former Young Muslim student activist Inayat Bunglawala (now of the MCB) reiterated the importance of the anti-Satanic Verses campaign, but said that he was wrong to call for it to be banned. Similarly, the MCB didn't call for the banning of Fitna, the anti-Islam film by the Dutch MP Geert Wilders, on the grounds that (as Bunglawala put it), the "same freedoms which allow Wilders to taunt Muslims so openly are also the ones which allow Muslims and others to spread the teachings of their faith".

The co-chair of the February 2003 Iraq war march, Anas Altikriti of the British Muslim Initiative, points out that the Qur'an says nothing about homosexuality beyond relaying the Biblical story of Sodom and Gomorrah. The Birmingham Respect councillor Salma Yaqoob has consistently opposed bans of and protests against anti-Muslim material. Influenced by Abdelwahab El-Affendi (author of Who Needs an Islamic State?) and the international scholar Tariq Ramadan, these Muslims are seeking to build a distinctly European Islam that sits easily with western pluralism and its political processes, without having to sacrifice the essentials of their beliefs.

So why is this narrative not trumpeted in the myriad guidelines on combating extremism? It's not Muslim views on halal meat or the hijab that bother the government, but their views on other matters. All these activists oppose the government's attacks on civil liberties. Like the 7/7 bombers, they were politicised not by Afghanistan or Iraq but by the Bosnian war, and the sight of western countries standing by while Muslims were dispossessed, raped and murdered on Europe's eastern doorstep. They see no reason to keep quiet about their views of western foreign policy now. As Yaqoob puts it, the huge support for the February 2003 march - particularly from middle England - led many Muslims to feel they belonged to Britain for the first time.

On these pages, Ziauddin Sardar has argued that the problem with the ex-Islamist Quilliam Foundation is not that it is anti-fundamentalist or anti-segregationist, but that it is anti-political; it wants Muslims to keep quiet. In fact, as Kundnani argues, a whole generation of British Muslims has rejected "the folkoric religio-cultural practices of their parents" in search of new ways of being Muslim, in public, in contemporary Europe. What could be more welcome?

• David Edgar is a playwright. Arun Kundnani's Islamism and the Roots of Liberal Rage is in the latest issue of Race & Class. The Institute of Race Relations holds a conference on Saturday to mark its 50th anniversary irr.org.uk