Michael Gove has suggested that Theresa May is turning a blind eye to the establishment of an Islamic Caliphate in Britain.  May, in response, has claimed that Gove is responsible for allowing the Muslim Brotherhood and the Jamaat Islami take control of Birmingham’s schools.  Furthermore, this spat of briefing and counter-briefing is all bound up with campaigns by May and George Osborne for the Conservative leadership.  Or so the more excitable commentary on yesterday’s spat between the two Cabinet Ministers has seemed to suggest.  The truth is more prosaic.

There is no disagreement between them on the Government’s counter-extremism strategy.  That’s to say, both believe that there should be one, and are signed up to the programme on tackling extremism published last autumn.  Under Labour, there was no such policy at all: no agreement over whether government should target extremism (that’s to say, the ideologies that inspire terror) as well as violent extremism (the terrorist acts themselves).  Hazel Blears and Ruth Kelly pulled bravely in one direction; John Denham and Jack Straw erroneously in the other.

David Cameron’s Munich speech was a bold and decisive break with this muddled past.  Gove agreed with it – and so did May.  As she told this site three years ago: “I take a very simple view that a violent extremist has at some point previously been an extremist, and by definition is an extremist, so you do need to look at that non-violent extremism.”  The differences between the two Ministers have been ones of degree, not direction.  The Education Secretary wanted a specific reference to “the teachings of the likes of Sayyid Qutb” in the policy.  He went above May’s head to Cameron, and got it.

This puts the briefing and counter-briefing from the two camps into the right perspective.  One Minister – Gove – likes to range outside his department.  The other – May – doesn’t want anyone meddling in hers.  It is a recipe for trouble.  The two have clashed in meetings, on this matter and others: the Education Minister rebuked his colleague after she set out a future leadership prospectus to last year’s ConservativeHome conference.  What seems to have happened on Monday is that Gove made some remarks at a lunch at the Times about past problems with policy and personnel.

Charles Farr, the director of the Office of Security and Counter-Terrorism, is not exactly a fan of the Munich policy.  In my view, he should have been moved after resisting it during the Zakir Naik controversy.  But Farr is able; the past is the past; May thinks highly of him, and he is working to deliver government policy.  Sources close to Gove insist that he said nothing critical of the Home Secretary’s present approach, but the Times got its story – and claims that he wants May’s job were thereby revived.

Like some real-life Daenerys Targaryen, the Home Secretary unleashed her dragons on her Cabinet colleague.  A scathing letter from her turned up in public, suggesting that the Education Secretary has failed to act on warnings of extremism in Birmingham schools, and an incendiary quote was supplied to support it: in effect, the missive suggested that he is all mouth and no trousers – grist to the mill of Gove’s shadow, Tristram Hunt.  And there you have it.  More to do with personality than policy.  And nothing much to do with George Osborne.  The Octopus Chancellor had no tentacle in this fight.

A statement was rushed out to soothe the fracas, but it had already disrupted one of the most sensitive slots in the political grid – Queen’s Speech Day.  How can further outbreaks be prevented?  Here are three pointers.  First, all concerned should be careful about what they say over lunch – and, bearing in mind the row over whatever Gove did or didn’t say about Boris Johnson to Rupert Murdoch, over dinner too.  Second, Hunt will take pot-shots at the Education Secretary whenever he can.  Conservatives shouldn’t supply him with ammunition.

Finally, we have yet to see what Ofsted’s report into Birmingham produces, and what has and hasn’t gone wrong since 2010.  But Gove can scarcely have been too tough and too lenient all at the same time.  He has appointed Peter Clarke, the former head of the Met’s Counter-Terrorism Command, to investigate the Birmingham allegations.  He has sent in Ofsted to do a separate report.  He has introduced an anti-extremism operation to the Education Department – one that simply didn’t exist before he took office.

He is already under attack from the Left over his response to the Birmingham claims.  It would be perverse were he also to be assailed now from the Right. Gove’s ideas for fine-tuning the anti-extremism policy should be considered on their merits.  For example, his friends are known to be concerned about the Government’s relationship with the Mosques and Imams Advisory Committee, within which the Muslim Brotherhood has a presence. The Saudis want the movement banned in Britain. That they want something isn’t automatically, or even usually, a reason to give it to them.

On balance, I suspect that a bar would be a mistake. But it would certainly be odd for the Government to ban it on the one hand and talk to its members within MINAB on the other.  In the meantime, the two Cabinet Ministers should quell a contretemps that has demonstrated the unquenchable intellectual self-assurance of the one (Gove) and the growing political self-confidence of the other (May).  First thing tomorrow morning, the Prime Minister should hang a sprig of mistletoe above his desk, summon both to his office, and get the unhappy couple to snog and make up.