One qualification Penny Mordaunt brings to the Department for International Development is her gap-year experience working in hospitals and orphanages in Romania after the 1989 revolution. But we can guess that the main reason for her promotion to the Cabinet is that she, like Priti Patel whom she replaced, was a Leave campaigner in the EU referendum.

Not that she was much good at that. Her most notable outing during the referendum campaign was when she insisted on live television that the UK couldn’t stop Turkey joining the EU. This was, as her leader and Prime Minister David Cameron gently pointed out, “completely wrong”, because the UK has the right to veto any country’s accession to the EU.

But the most important consideration in this minimal reshuffle was to maintain the balance in the Cabinet between Remainers and Leavers. Of the 22 full cabinet members, seven advocated leaving the EU, and Theresa May knew that if she allowed that number to fall to six there would be a backlash from Eurosceptic Conservative MPs.

Having experienced the fury of Tory MPs upset by last week’s promotion of Gavin Williamson, the chief whip, to head the Ministry of Defence after Michael Fallon’s resignation, May did not want to risk that again. The reaction to Williamson’s appointment came mainly from those MPs resentful of his closeness to the Prime Minister and lack of experience as a departmental minister. At least Mordaunt has served in two departments, defence then work and pensions, and was a minister of state, the rank just below cabinet status.

But it is her status as a Brexiteer that was probably decisive. Assuming that May would not countenance a cut in the number of women in the Cabinet, Mordaunt was the only female Brexiteer at minister of state level. If it had not been for those considerations, Alistair Burt or Rory Stewart, already DfID ministers and both Remainers, might have been better qualified.

Priti Patel out: Theresa May forces International Development Secretary to quit

This second mini-reshuffle in a week confirms May’s weakness. She has to manage the Tory factions as if they were separate parties. The coalition of Leavers and Remainers is as real as that between Tories and Liberal Democrats from 2010 to 2015, when Tories would have to be replaced by Tories and Lib Dems by Lib Dems.

But May’s middle position is as much a strength as a weakness. She straddles the Leave-Remain divide as one of the most reluctant Remainers before the referendum who has since sought to deliver an uncompromising version of Brexit. That means neither side wants to oust her, for fear she would be replaced by a leader from the enemy.

May has often been compared to John Major recently, who also held together a Tory government divided on the question of Europe for longer than seemed possible. But the truth about Major is that, although he appeared to be holding the ring between the pro-EU and Eurosceptic factions, he was really on the pro-EU side. So far May has managed to avoid revealing whether she really stands with those who want to stay close to the EU after we leave or with those who want the freedom to diverge from EU rules.

Sooner or later, May will have to choose sides in her own party’s civil war. But today she continues to be even-handed between them.