A Commons vote affirming confidence in Her Majesty’s government does not indicate that parliament trusts Theresa May. Her reprieve on Wednesday night, by a margin of 19, largely expresses Tory and DUP reluctance to risk a general election. Power is still flowing away from the prime minister.

In 2017 voters deprived the Tories of a majority. Last December the government was found in contempt of parliament. One-third of Tory MPs have said they have no confidence in Mrs May as their party’s leader. On Tuesday, the prime minister’s Brexit deal was crushed in a Commons defeat greater than any recorded in the modern era. Mrs May’s authority has been stripped away; her credibility is gone. Every precedent guides her towards resignation. But not much about Brexit follows precedent.

Immediately after Wednesday’s vote the prime minister offered talks with leaders of opposition parties to break the impasse. It is a welcome shift in tone, but there is no indication from Mrs May’s record that she has the diplomatic skills required to make such a consultation fruitful. She has clung compulsively to her original negotiating “red lines” and still seems unaware that the Brexit model they defined is beyond resuscitation. Her resistance to compromise has ratcheted up the risk of Britain reaching the article 50 deadline without any deal.

Despite Mrs May’s new overtures, Downing Street still formally rejects the prospect of a customs union with the EU, although softening that line would transform dialogue with Labour and pro-European Tories. A customs union alone does not dissolve obstacles in the Commons, nor does it resolve problems around the Irish border, but it is the foundation of any Brexit deal that stands a chance of achieving those goals. Mrs May’s objection is that it limits independence in trade talks and upsets hardline Tory Eurosceptics. But the UK’s leverage in talks with superpower blocs – the US, China, India, the EU – is vastly overstated and the Brexit hardliners will never be satisfied with any deal. Holding out for their approval is a waste of time.

Mrs May speaks often about duty to the electorate, as if the choices she makes stand above party interest. The opposite is true: she has imprisoned herself in a narrow, parochial view of what Brexit means, conditioned by irrational attachment to the Tory right. It is imperative that she break free of those constraints. She must show sincerity in the offer to work across the house, which means giving serious consideration to proposals that cross the red lines: a customs union, Efta, the EEA or some combination of those institutional arrangements.

There are models of a soft Brexit that have been developed by groups of Labour and Tory MPs, showing the bipartisan spirit that Mrs May lacks. Wednesday’s fierce no-confidence debate stoked fires of tribal party allegiance, but those flames cannot be allowed to consume the prospect of Brexit partnership. The government’s next step must be to engage with the authors of alternative Brexit blueprints and present them in parliament as a menu of options, subject to indicative, unwhipped votes. MPs must, in the first analysis, be allowed to coalesce around plans unconstrained by formal party lines. The Commons should consider how such ideas might be developed with wider popular consent, as envisaged in the innovative model of a citizens’ assembly. The public could then be given a final say on the choices available, including EU membership on current terms.

That process demands an extension to the article 50 period. Even an off-the-shelf Brexit model needs enabling legislation, which takes time. The prime minister’s reluctance to admit as much is another symptom of her delusional obstinacy. Mrs May has routinely struggled to adapt to changing circumstance as events have progressively limited her room for manoeuvre. That rigidity seems intrinsic to her character, irrespective of invitations to cross-party talks. It is not enough to affect a change of tone in the aftermath of a fierce parliamentary debate. The shift in style is welcome and long overdue. But the prime minister must now urgently show readiness to compromise on the very substance of Brexit.