One important detail of Theresa May’s deal with the Democratic Unionist Party went unnoticed – that it was not May, but the Conservatives’ Chief Whip, Gavin Williamson, who signed the accord, alongside his opposite number, the DUP MP Jeffrey Donaldson.

That highlighted two things: firstly that the Conservative Party is already planning for life after May. The deal runs for two years and is bound to the party, not the leadership of Theresa May. The second is that while May is the Prime Minister, it is the Conservative Party that runs the show.

That’s an important thing to remember about today’s confusion about whether or not the government will end the freeze in public sector pay, where raises have been capped at one per cent since 2012 and have effectively been frozen in real terms since the financial crisis.

Michael Fallon, the Defence Secretary, signalled that the government could end the freeze, as did Chris Grayling, the Transport Secretary. (For what it’s worth, Gavin Barwell, now Theresa May’s chief of staff, said before he took up the post that he thought anger at the freeze contributed to the election result.)

In terms of the government’s deficit target, it’s worth remembering that they can very easily meet Philip Hammond’s timetable and increase public sector pay in line with inflation. They have around £30bn worth of extra wriggle room in this year alone, and ending the pay cap would cost about £4.1bn.

So the Conservatives don’t even have to U-turn on their overall target if they want to scrap the pay freeze.

And yet Downing Street has said that the freeze remains in place for the present, while the Treasury is also unenthusiastic about the move. Which in the world before 8 June would have been the end of it.

But the important thing to remember about the government now is effectively the only minister who isn’t unsackable is the Prime Minister. What matters is the mood, firstly of the Cabinet and of the Conservative parliamentary party.

Among Conservative MPs, there are three big areas that, regardless of who is in charge, will have to change. The first is that they will never go into an election again in which teachers and parents are angry and worried about cuts to school funding – in other words, more money for schools. The second is that the relationship with doctors needs to be repaired and reset – in other words, more money for hospitals.

The government can just about do all of those things within Hammond’s more expansive target. And regardless of what Hammond stood up and said last year, what matters a lot more than any Downing Street statement or Treasury feeling is the mood of Conservative MPs. It is they, not May, that pulls the strings now.