Prime ministers do not get to dictate their legacies from a lectern outside No 10, and there was some pathos in Theresa May’s attempt today to list accomplishments in government to offset her colossal failure to take Britain out of the European Union. That she oversaw a reduction in the use of disposable plastics is laudable, but it is not how history will remember her time in office. But Mrs May never saw Brexit as her sole purpose in Downing Street. Her inability to grasp from the outset how all-consuming and difficult the project would be played a large part in her downfall.

She was poorly advised by ideologues who thought a hard Brexit could be achieved at minimal cost, but that is no excuse. She chose to take the bad advice when it chimed with her own prejudices and rejected wiser counsel. She entered negotiations in Brussels ill-prepared and was schooled in brutal realities of economics and diplomacy. That was humiliating enough, but her failure to pass those lessons on to a national audience was unforgivable. If she did understand the cruel calculus of Brexit trade-offs, she did not confront her party with the truth. Nor did she use the amplifying power of her pulpit to shape public understanding of the issues. She preferred vacuity and dishonesty – “Brexit means Brexit”; “No deal is better than a bad deal”. She decommissioned the truth, afraid it might be used as a weapon against her.

Play Video 2:01 As Theresa May resigns, how will she be remembered? – video

The country now faces a Conservative leadership contest fought in a fact-free arena. The candidates must appeal to their parliamentary colleagues and then to a membership numbering little more than 120,000. That electorate is not by any measure representative of the country, being older, whiter and richer than the average citizen. A majority of card-carrying Conservatives are also happy to proceed with a no-deal Brexit, perhaps because they are financially insulated from its appalling consequences or because they do not believe the dangers are real.

They will demand reckless pledges before handing the keys to No 10 over to the next prime minister. That could be Boris Johnson, the bookmakers’ favourite, or someone who outmanoeuvres the former foreign secretary by co-opting some of his bogus arguments. The Tory leadership contest will burden any victor with commitments that militate against a solution to the Brexit crisis – a promise to renegotiate the withdrawal agreement, for example. That will not happen. The EU is not going to retreat from its current position at the behest of a radical Eurosceptic British leader animated by ideological hostility to the European project.

Unless Mrs May, by some remarkable twist of circumstance, gets her Brexit deal through parliament in the coming weeks, her successor will quickly confront a familiar menu of options: Brexit via the deal that exists, Brexit with no deal, or abandoning Brexit altogether. That new prime minister will also confront the same parliamentary arithmetic that obstructed Mrs May’s efforts to achieve consensus. The new leader will have no mandate from the country and no majority in the Commons. The likelihood of an early general election or another referendum has therefore risen, even if the exact route is still unclear.

In her valedictory address today, Mrs May spoke of compromise as a noble pursuit, and she was right. Polarisation and radicalisation are making Britain ungovernable. But unifying the country around any one version of Brexit is not technically possible. It is an ambition Mrs May arrived at late, by which point she had no political capital left to spend. Leaving the EU is not a vague, malleable objective. It comes down to precise legal choices. Mrs May made her choices and parliament rejected them. Her successor will face equivalent choices in a hostile climate where continental goodwill and domestic public patience are spent. It was once within her power to reframe the debate around goals that were more achievable, but she refused that challenge. So she passes on an insoluble problem to a successor who can only win the job by promising to do the impossible. It is a miserable and poisonous legacy.