As every middlebrow with a newspaper column or Radio 4 slot to fill agrees, a vulgar "new atheism" is sweeping Britain. The readers of Richard Dawkins, Philip Pullman and Christopher Hitchens are, they tell us, crass because they do not appreciate the mystery of religion, the consolations of ritual and all the rest of it, and also dangerous because they are as fundamentalist in their criticisms of religion as the religious fanatics they criticise.

I could waste your time by pointing out that "new atheists" are not so different from old atheists – we still don't believe in God, for instance – and add that the charge of moral equivalence would be easier to substantiate if atheists planted bombs on the underground. But space is short and the depressing truth about "new atheists" no one dwells on is that if they exist outside the imaginations of religious writers, they are never there when you need them. For if we had a vibrant atheist or secularist movement in Britain, it would now be tearing into this government for once again trying to ride the Islamist tiger.

Last Sunday, John Denham, the communities secretary, announced: "Anyone wanting to build a more progressive society would ignore the powerful role of faith at their peril. We should continually seek ways of encouraging and enhancing the contribution faith communities make on the central issues of our time."

As the week wore on, it became clear what type of "faith communities" Labour wanted to put at the centre of its "progressive society". Denham is forcing out of his department Azhar Ali, an adviser from the heart of the Labour movement (he was once the Labour leader of Pendle council). Ali's crime was that he opposed Islamism while advising Tony Blair, Ruth Kelly and Hazel Blears.

After Daud Abdullah, the deputy general secretary of the Muslim Council of Britain, signed a declaration advocating attacks on the Royal Navy if Gordon Brown sent ships to impose an arms blockade on Gaza, Ali told his comrades to cut all links. He might have said that a centre-left party should never have had links with the MCB in the first place. It contains supporters of the Arab Muslim Brotherhood and the south Asian Jamaat-e-Islami. Arab liberals know the Brotherhood to be the enemy of every enlightened value they hold, while their Bangladeshi equivalents regard Jamaat in the same way Observer readers regard the BNP, only worse because Jamaat murderers collaborated in the Pakistani army's crimes during the Bangladeshi war of independence.

That brief moment of principled politics is over. There's talk of the government giving the MCB's Sir Iqbal "death perhaps is a bit too easy for Salman Rushdie" Sacranie a peerage. Meanwhile, ministers are about to cut financial support for Sufi Muslims who, like the majority of Britain's Muslims, Sunni or Shia, are not represented by the MCB.

The fix is in and Islamists are all over Whitehall again. Denham is entertaining Inayat Bunglawala of the MCB, who gave a taste of the "progressive" policies Labour is encouraging when he wrote an article defending Sheikh Yusuf al-Qaradawi, spiritual leader of the Muslim Brotherhood, and a preacher who recommends wife-beating, genital mutilation of girls and the murder of apostates and homosexuals. Earlier this year, the sheikh said of Adolf Hitler's massacre's of the Jews: "This was divine punishment for them. Allah willing, the next time will be at the hand of the believers."

Astute outsiders look at people who were on the 20th-century left and notice that they have gone from calling themselves "socialists" to "social democrats" to "third wayers" to "progressives" in rapid succession. They might have wondered what the new "progressive" label means. Now they know.

Over at the Department for Children, Schools and Families, Ed Balls is as keen on appeasing the churches as Denham is on appeasing radical Islam. Last week, the National Secular Society (of which I am a patron) described how Labour allowed faith schools to reject applications from non-religious teachers solely on the grounds that they doubted the presence of supernatural beings or worshipped the wrong supernatural being. The rebuttal Balls's department issued was so vituperative and inaccurate that civil servants had to take the virtually unheard-of step of withdrawing it and thus tacitly acknowledge the truth of the secularists' claim that the only people New Labour allowed employers to discriminate against were atheists and sceptics.

You don't need to be a political tactician to understand Labour's dog-whistle politics. Balls is playing both sides by alleging that the Tories would bring creationism to the classroom while doing nothing to restrict religious control of schools. At the Department for Communities, I am told that real power does not rest with the ineffective John Denham, but Shahid Malik, his deputy, who perhaps hopes that appeasing Jamaat and the Brotherhood will help him keep the core vote in his Dewsbury seat and enable a few other desperate Labour MPs to survive a potential Tory landslide as well.

No minister, though, imagines that they will pay a political price as hundreds of thousands of "new atheists" walk away in disgust. Which is not to say that a price will not be paid, just that it will come in a coinage no Observer reader should want to accept. Communalist politics do not always generate a liberal backlash; more often, communalism merely produces heightened communal tension.

Sufis are now promising to tell Dewsbury Muslims not to vote for Malik, which is no more than he deserves. More seriously, a revival of the left's affair with Islamism can only help the BNP by convincing the white working class that their rulers hypocritically denounce racial conspiracy theories, misogyny and homophobia when they come from the followers of Nick Griffin, but not when they come from the friends of Yusuf al-Qaradawi.

It is a dismal way to imagine Britain's longest period of left-wing rule ending, but perhaps it will take the BNP winning a parliamentary contest or so splitting the Labour vote that the Tories come through the middle in "safe" seats for the party to realise you cannot be a fairweather anti-fascist or part-time leftist without your "progressive society" turning to dust.