This reshuffle suggests Boris Johnson is heading for an early election

This is an over-the-cliff reshuffle. It is, as Boris Johnson said in Downing Street, about leaving the EU, “no ifs or buts”. It is a “throw everything at the problem and hope it works” reshuffle. It is a “make the Brexiteers own it” reshuffle. Except Penny Mordaunt and Liam Fox, because they went over to the other side, by supporting Jeremy Hunt.

Our new prime minister is trying to do so many things at once that we are bound to wonder if he is trying to distract us from his lack of a plan. Sacking half the cabinet and bringing Dominic Cummings – played by himself, not Benedict Cumberbatch, this time – into No 10 is designed to administer electric shock treatment to the Whitehall machine.

The machine has become stuck, gummed up by inertia and deliberate sabotage by Remainers, according to the hardcore Leaver mind – the hive mind of the insurgency that has now taken over the levers of the state.

So Johnson has taken ministers who know something about their brief and sacked them – because, although they voted Leave in 2016, they have shown insufficient revolutionary ardour – in the belief that this will inject urgency into the veins of the mandarinate.

It is just possible that going to war with the civil service, the Remain wing of the Conservative Party, and the Insufficiently Fervent Leave wing of the Tory party simultaneously is not going to end well.

But for the moment, the new prime minister is pressing ahead with vim, vigour and other words beginning with V, confident that “the doubters, the doomsters, the gloomsters”, as he put it, will be scattered before him.

It turns out that the appointment as chief whip of Mark Spencer, the self-effacing and Remain-voting MP, was a feint in the direction of unity and pragmatism. The real appointments were made today, and they lurch in the direction of division and Brexit purism.

The most important was Dominic Cummings, the director of the Vote Leave campaign, and one of the most unusual personalities to have been involved in government in recent years. I could not believe he was back until I saw him, in his T-shirt, in the photos of No 10 taken just after Boris Johnson arrived back from the Palace.

His appointment is a statement of intent: his contempt for much of the civil service and most soggy politicians is well known.

And you can see the logic behind giving big jobs to Priti Patel and Theresa Villiers – they are two of the 28 Tory Eurosceptics who voted against Theresa May’s deal at all three times of asking. Bring them into the government and they will have to vote for whatever rebadged version Johnson negotiates.

But beyond that, the idea that Johnson has a plan disintegrates the moment it is subjected to the idlest consideration. By going hard over Brexit, Johnson is likely to add to the numbers in Justine Greening and Dominic Grieve’s little band of five pro-Europeans who are going to vote against any form of Brexit. (They will be six until Jo Johnson returns to government – but promoting members of his family will not secure Boris all the votes he needs.)

Nor is he making it any easier to win over the extra Labour votes he needs.

So perhaps that is the plan. Throw everything at Brexit, and if it doesn’t work, go to the country with a hard-Brexit manifesto and a pact with Nigel Farage to ask the people for a true believers’ mandate.