Just like that, she’s gone. Theresa May, the least successful British prime minister in living memory, has resigned.

So much agonising, so much plotting, so many secret plans to get rid of her over so many months have failed. But after a European parliamentary election in which her Conservative Party crashed to historic lows, she has finally thrown in the towel.

Bizarrely, she wants to hang around so that she can host Donald Trump in early June — her reasoning here, as in so many other areas, is unfathomable — and then she will go.

The race to replace her is already on. Boris Johnson’s leadership campaign has been hiring staff for many weeks. Dominic Raab, another candidate — there are at least a dozen — has had himself photographed, with his wife, in his lovely pastel kitchen. Several of her Cabinet ministers have already started to hit the television studios.

It’s an odd campaign: the only people who get to vote in this election are the paid-up members of the Tory party, some 124,000 people. According to the rules, they will choose between two people nominated by Conservative Members of Parliament. This tiny group of people will decide who runs the nation.

Will it be a so-called hard Brexiteer who will break all of Britain’s trade relationships overnight, or perhaps a “Remainer” who will seek a way back in to the European Union? Or perhaps a compromise between the two?

But, although that seems like a big choice to give to a small number of people, the reality is rather more banal. In truth, whoever replaces May will face exactly the same choices and exactly the same dilemmas as she did.

A British prime minister who decides to crash out of the EU with no treaty arrangements on a Monday will wake up on Tuesday to discover that their immediate priority is ... to write a new treaty with the EU.

A British prime minister who wants to forge a reasonable compromise will discover that there is no majority for any compromise, reasonable or unreasonable, in the present House of Commons.

A British prime minister who wants to remain in the EU will immediately face a wave of outrage from the one-third of Britons who have just voted for the brand-new “Brexit party”.

All of the constraints remain. All of the conundrums are unresolved. It is still the case that Britain cannot both exit the all-European customs union and keep open the border between Northern Ireland and the Irish republic. It is still the case that there is no Brexit “deal” that makes Britain richer, and certainly not £350 million (about $445 million) a week richer, as the Brexit referendum slogan in 2016 claimed.

It is not a coincidence that none of the Tory leadership contenders can present a concrete plan, because there can’t be one. The only conceivable game-changers are another referendum, which “Remain” might win, thus alienating a part of the Conservative Party for ever — or another General Election, one that the Conservative Party, on present performance, will lose.

There is not much point in wishing good luck to May’s successor, in other words, because it’s unlikely to help.

• Anne Applebaum is a Washington Post columnist, covering national politics and foreign policy, with a special focus on Europe and Russia. She is also a Pulitzer Prize-winning historian and a professor of practice at the London School of Economics. She is a former member of The Washington Post’s editorial board