Theresa May has rounded on the European Commission and her fellow heads of government in a speech which takes the United Kingdom ever closer to leaving the European Union without a deal.

The Prime Minister, whose proposals for the final Brexit deal have no realistic prospect of winning a majority in Parliament or winning support in the European Union, called on European member states to lay out their own proposals for the final EU-UK relationships in an astonishing statement that at times appeared to be barely adjacent to reality.

The truth is that the other 27 member states and the Commission have been crystal clear: the United Kingdom can either have a distant “low regulatory freedom, high market access” arrangement or Norway style deal, or a “high regulatory freedom, low market access” arrangement in the manner of Canada.

A Canada-style deal would require either a regulatory border in the Irish Sea – unacceptable to the DUP, whose support is vital to sustaining the Conservative government in office – or a hard border on the island of Ireland itself, unacceptable to Ireland, which as a member state holds a veto over the final free trade agreement. Neither arrangement could secure a majority in the House of Commons as it currently stands. The so-called “backstop” agrees that, in the event that the EU and the UK are unable to reach an agreement, Northern Ireland will remain within the regulatory orbit of the European Union, creating a regulatory border in the Irish Sea: an arrangement that May now describes as unacceptable despite having signed up to it in December 2017.

May’s Chequers’ proposals - which she doubled down on - please nobody. In the United Kingdom, they contain far too great a degree of rule-following for supporters of a Canada-type arrangement, but they provide too little market access to be supported by those who want a Norway-style deal. As far as the EU goes, the pick-and-mix of rights and obligations that May chooses are also unacceptable, as member states fear they risk unravelling the single market.

Is there any hope of avoiding a no-deal exit? Optimists will hope that the important part of May’s speech was not the sabre-rattling but the brief statement that the United Kingdom will bring forward alternate proposals to the backstop that maintains the territorial integrity of the United Kingdom: likely a proposal that the whole of the United Kingdom would have full regulatory alignment with the bloc in the absence of agreed solutions. But with so much goodwill eroded among the EU27 and with that deal very far indeed from what Conservative Brexiteers want, it is unclear whether that arrangement could win support among the EU, let alone at Westminster.