Senior civil servants in the Home Office have accused the Department for Education (DfE) of running a "parallel security policy", Newsnight has revealed, after years of rivalry between the two ministries over how to deal with extremism.
Part of the argument is a real difference of opinion over extremism - Michael Gove would oppose a wider range of views and actions than Theresa May. He is more worried about the idea of a "conveyor belt" from religious conservatism to extremism.
There is, however, also a simple turf war at the centre of this. Mr Gove has some cover to intervene in policy in this area by dint of being a member of some relevant ministerial committees. But Mrs May's officials feel he has, from time to time, overstepped what is appropriate.
For example, Newsnight has also uncovered a bitter argument over the funding of the Quilliam Foundation, a think tank that supports Mr Gove's views.
In March 2011, the Home Office refused to continue funding the body, which had enjoyed public support, and which then said it needed £150,000 to keep working.
On the offensive
Defending that decision, Damian Green, a Home Office minister, said that "Quilliam should be free to contribute to the wider debate, but not depend on government funding to do so".
Shortly afterwards, however, the DfE stepped in. Its ledgers confirm that, in May 2011, it contributed £120,000 to the think tank.
This week, Mrs May has been on the offensive. She wrote a letter, published by the Home Office, to the DfE.
It suggested some of the problems that were uncovered following the "Trojan Horse" saga in Birmingham, when schools were investigated over extremism, might be the fault of the DfE.
As a result, one senior mandarin at the DfE likened her to Carlos Alberto, a long-retired Brazilian defender.
It may not be an obvious comparison, but the player is best known for a famous attack in the 1970 World Cup where he scored a goal after appearing out of nowhere on the right wing.
The prime minister is stepping into this argument to cool it off, but there are two important legacies; first, it has established Mrs May's political confidence. The tone of the letter is rather haughty.
Second, it has created a rod for Mr Gove's back. The letter says that "allegations relating to schools in Birmingham raise serious questions about the quality of school governance and oversight arrangements in the maintained sector".
That's going to be problematic for Mr Gove long after the dust has settled here; that's because it seems that Mrs May supports Labour's view that the DfE does not have adequate capacity to keep an eye on the whole school system.
An attack from the right might just have caused problems for the Tories from the left.