“Let all the poisons that lurk in the mud hatch out”: the muttered incantation of the emperor in Robert Graves’s Claudius the God has rarely seemed so apposite. It is time for this government to drop the pretence that it is healthy and functioning. A reckoning is long past due. Daily, we see a new pustule or sore – on some days several. According to the Sunday Times, the Brexiteers are plotting to install Boris Johnson as prime minister, Michael Gove as his deputy and Jacob Rees-Mogg as chancellor. The last of those would be especially contentious, since the Moggster has spent much of the past week accusing the Treasury of “fiddling the figures” in its analysis of Britain’s prospective departure from the EU.

Yet – as if to pave the way for an ideological purge of Her Majesty’s Treasury – the leading Brexiteer MP Bernard Jenkin accuses Philip Hammond in the Sunday Telegraph of trying to countermand the prime minister’s argument that we should leave the EU customs union. For those Tories who (mysteriously) regard Brexit as the path to a New Jerusalem, the chancellor’s call in Davos for only “very modest” changes to the UK’s relationship with the EU is simply a provocation too far.

It has become a grotesque pantomime. Tory remainers demand Johnson’s head every time he intervenes – as he did last month, briefing the press that the NHS should be given £100m extra a week as a downpayment on what the foreign secretary still insists will be a grand Brexit bonanza. Whenever Hammond seeks to salvage this or that element of Britain’s economic relationship with Europe, he is accused by leavers of disregarding the “will of the people”.

Few Tories now dispute the length and gravity of the charge sheet against Theresa May: a disastrous general election, a terrible party conference and a reshuffle that merely advertised her weakness. The argument that her resilience is somehow noble is made much less frequently: in the midst of such political mayhem, it looks increasingly like stubborn political delusion.

‘She is the stuffed remnant of a once-optimistic prime minister. This is government by taxidermy.’ Photograph: Vianney Le Caer/Rex/Shutterstock

Still, though, one continues to hear that she should stay where she is, as the only senior Tory who can realistically preside over the “constructive ambiguity” required by the Brexit talks – publicly demanding a clean break while quietly negotiating the complex, nuanced and unheroic deal that anyone remotely sensible knows is the only halfway palatable outcome.

The trouble is, she is doing no such thing. She is not the deft manager of meaning, soothing all sides and persuading each faction that its interests are being respected. She is the stuffed remnant of a once-optimistic prime minister, helpless in the midst of anarchic cacophony. This is government by taxidermy.

It is no longer plausible to argue that a formal test of her leadership would be a fatal disruption of the talks with Brussels. Without a decisive answer to the question “Who leads, and where?” I do not see how those talks can meaningfully proceed. We are an international joke, at risk of being taken to the cleaners by the EU or left with no deal at all. In such circumstances, clarification is not a distraction but precisely the opposite.

Were I in May’s shoes, I would pre-empt a confidence vote and – in the manner of John Major in 1995 – demand one myself

Were I in May’s shoes, I would pre-empt a confidence vote forced by letters from 48 of my own MPs, and – in the manner of John Major in 1995 – demand one myself (if necessary by instructing sympathetic backbenchers to trigger the process). I would then set out an explicit, unambiguous and unapologetic strategy for Brexit, and instruct the Conservative parliamentary party to back me or sack me.

Let us say, as seems quite probable, that MPs sacked her, as they did Iain Duncan Smith in 2003. There would then be a period of bedlam as the Tory party fought with teeth bared and daggers drawn to settle not only its future but the future of Britain’s relationship with the EU. It would be ugly, protracted and almost entirely destructive.

Would the answer that emerged at the end be sustainable? Would the new Conservative leader – and, if the Commons pact with the Democratic Unionist party held – prime minister be able to provide the discipline and clear sense of trajectory that has been so conspicuously lacking under May? Quite possibly not. But that is the whole point. It may well be that the Tory party, as presently constituted, is structurally incapable of meeting the patriotic needs of the hour. It really is for the Conservatives, and not the rest of us, to prove that this suspicion is unfounded.

At any rate, the present arrangement is a hideous international embarrassment. It seems to me painfully obvious that we need an extension of the negotiating period set by article 50 – entirely possible under its section 3 – if only to replace panic with some semblance of deliberation. And, sooner rather than later, there should be another general election.

I am scarcely Jeremy Corbyn’s greatest fan, but the notion that the status quo must be preserved simply to thwart his chances of becoming prime minister is not only democratically contemptible but morally outrageous. Indeed, the prospect of a fresh election would force Labour, at last, to spell out its plans for Brexit, and embrace the risks of clarity.

Yes, I know the voters are fed up of trudging to the polling booths. But they’ll be even more fed up if Britain sleepwalks into a second-rate status, with all that implies, because a clinically dead government was permitted by a mixture of squeamishness and boredom to remain on life support. Time to flick the switch and see what happens.

• Matthew d’Ancona is a Guardian columnist