With a screech of finger nails, Theresa May's hands were finally prised from the Number Ten desk last week, but she still has a kitten heel jammed in the front door. In a tense and tearful confrontation with the Tory backbench 1922 Committee she finally agreed to leave office under an agreed timetable. Only this agreed timetable will not actually be agreed for another two weeks - which leaves her with the remotest scintilla of a chance of remaining in office.

Her last hope is a Damascene conversion on the road from the European elections by backbench MPs – Tory and Labour - and her coalition partners in the DUP. These elections to a parliament the UK is supposed to have left already, were always a disaster waiting to happen. Nigel Farage's Brexit Party has now stormed ahead, threatening the very existence of the Conservatives as a governing force. The Tories will be humiliated this week in what is likely to be their worst showing in any national election since 1906.

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But deep in the bowels of Theresa, hope springs that the scale of the defeat just might persuade Tory MPs to vote for her EU Withdrawal Bill, at its fourth and final outing. She hopes they'll realise that a continuation of the Brexit deadlock could lead to the loss of their seats at the next general election. However, few appear convinced that keeping a hold of May will save their well-upholstered derrieres. The nation as a whole is so fed up with her robotic delivery, and sense of her own indispensability, that keeping her in office, even for a few months, would be just as damaging.

Even the thought of Boris Johnson taking over as Tory leader and Prime Minister is not enough to save her. This is admittedly a prospect that many, even in her own party, find about as congenial as having Donald Trump in Number Ten. But at least Boris would be someone different to loathe. Anyway, there's no guarantee that Boris Johnson will be the successor to May as party leader.

He lost it in 2016, after his prevarication and incompetence led his Brexit lieutenant, Michael Gove, to knife him in the back. When history came to call, Boris Johnson was out to lunch. He went on to perform poorly as Foreign Secretary, and then returned to his lucrative career as a columnist, where he aroused fury by comparing Muslim women in Burqas to letterboxes and bank robbers.

Johnson is clearly the favourite among the Tory Party membership, who don’t believe in islamophobia. However, he has alienated many Tory MPs and they control the method of election. Under the rules, MPs must first give their verdict on the candidates. Only the top two get the chance to submit themselves to a vote of the wider Tory membership. The anyone-but-Boris campaign is already gaining momentum.

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Actually, in rejecting Boris Johnson, the Tories would probably be making a mistake. Like him or loathe him, he is the only figure in the dull-as-ditchwater cabinet that has any popular recognition. He was, after all, elected twice as London Mayor, and is actually quite liberal on issues like LGBT rights and immigration. His is at least a familiar face in a race of also rans.

Never has the decline of UK politics been more evident than in the ministerial ranks of the governing party. Senior ministers like Jeremy Hunt, Dominic Raab and Liz Truss, who've been shamelessly parading their dubious virtues in the press, have said and done little in their careers that is memorable. The Foreign Secretary's claim to fame is that BBC presenters keep confusing his surname with female genitalia. Dominic Raab, as Brexit Secretary, admitted he hadn't read the Good Friday Agreement. Liz Truss referred to the Environment Secretary as “wood burning Gove”, and once expressed manic outrage about cheese imports.

Would any of them do a better job than Theresa May? Well, that isn't really the issue. When a Prime Minister loses the support of the Commons, most of her cabinet and the voting public, the only honourable course is to resign. This is so that someone else can come in, untainted, with a new policy. Only Theresa May has been too incompetent to manage even her own resignation, as the SNP Westminster leader, Ian Blackford, pointed out last week.

The announcement gave Labour an excuse to leave cross party Brexit talks they'd never seriously wanted to succeed. They were able to say that there's no point when the Prime Minister's authority has evaporated. Jeremy Corbyn doesn't have a lot of authority either, and has been facing both ways on Brexit for so long he doesn't know whether he's coming or going. But he isn't the government.

Theresa May's belated resignation also makes it almost certain that her Withdrawal Deal will be rejected again, if and when the Speaker, John Bercow, allows her to try for a record fourth defeat in a row. Why would MPs vote for her deal when there is the prospect of another leader taking over in a matter of weeks? Someone who might take a tougher line with Brussels?

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With the Brexit rebellion raging, after Nigel Farage's success this week, why would Tory MPs suddenly vote for a deal they have themselves been saying is “worse than staying in the EU”? It would make little sense. Nor would another round of indicative votes, which appeared in a leaked document prepared for the cross party talks, be likely to salvage Theresa May's Brexit deal. Which means that Britain's Brexit deadlock is likely to continue.

Once the Tory leadership race is formally announced, it will occupy MPs till the Summer Recess. Then we have the party conference season, at which the new Tory leader, probably an anti-European, will be promising a “managed” No Deal Brexit on WTO terms. But this is just as unlikely to get the support of parliament when it returns in September.

Brussels will anyway not reopen the Withdrawal Agreement, even for a free trade deal. Why would they? The WA is not about the future trading relationship, but about the divorce settlement: money, citizenship and the Irish Border. Eventually, parliament is going to have to recognise that something very similar to Theresa May's deal will have to be passed before Britain can escape from Brexit purgatory.

The deadlock can only be broken in one of three ways: accepting the Withdrawal Agreement, another referendum, or by revoking article 50 and staying in the EU. There is no parliamentary majority for any of these options, of which my personal favourite would be revoke. A general election isn't really a solution, unless Labour agrees to campaign in it for a referendum, which Jeremy Corbyn opposes, and wins. And even then, a referendum might not deliver the result Remainers hope for.

Britain is still scheduled to leave the EU on Halloween at the end of October. It is beginning to look as if nothing will have been resolved by then. In which case, Britain could be stuck in the EU, and subject to its laws, without any representation in Brussels. Mind you, purgatory isn't so bad once you get used to it, and it's surely better than Brexit.