William Petty, the 2nd Earl of Shelburne, is one of the less well-remembered people to have been a tenant of Number 10. I mention him because, as Tory MPs argue about how long they should give Theresa May, the brief, but illuminating lifespan of that 18th-century prime minister is a possible guide to her future.

Shelburne was propelled into office after Britain suffered the enormous humiliation of losing the American war of independence. Lord North had to resign as prime minister and someone was needed to perform the thankless task of negotiating a peace with the ex-colonies. Shelburne put his lips to that poisoned chalice. He decided that Britain’s long-term interests were best served by having a thriving trade relationship with an expanding and prosperous United States. Most historians salute him for this act of visionary statesmanship, but it won him few friends in a parliament that thought the territorial settlement to be excessively generous to the United States. Once the Peace of Paris was agreed, Shelburne was ejected from Number 10 and spent the rest of his life moaning that his career had been a failure.

History does not repeat itself, but you can sometimes catch a rhyme. So we can think of David Cameron, the man who destroyed his premiership by accidentally amputating Britain from the European Union, as the Lord North of our times. Theresa May is the Shelburne, a friendless premier kept on at Number 10 for the duration of the withdrawal negotiations and destined for defenestration as soon as they are completed.

This is one strand of thought in the febrile hive mind that is the Conservative party. It sees a version of Mrs May’s future that goes something like this. Brexit will be accompanied by a host of setbacks, retreats, disappointments, compromises and crises. And that will be so even if the horrendous process of extricating Britain from the EU is not an unmitigated disaster. Someone has to absorb all the toxic feeling that this will arouse. Someone also has to endure the weekly torture that will come with attempting to get all the Brexit-related legislation through parliament when the government does not have a reliable majority. Since it was Mrs May who landed the Tories in this predicament by messing up the election, it is only appropriate that she should be the human sponge who soaks up all the blame. This will be a thankless and joyless role, but she made it her fate and at least she will get to be prime minister for a bit longer. Then, when the Brexit job is done, the Tory party will bid her thank you and goodnight. Mrs May will be consigned to a Shelburne-like obscurity and the Conservatives will install a fresh leader to try to rejuvenate the party in time for the next election.

This raises the question whether Mrs May can bear the thought of carrying on like this. It is a highly unappealing prospect to be a prime minister who is the prisoner of her colleagues, lingering at Number 10 until her party decides to dispatch her. She knows that her authority has been eviscerated. She knows that none of her colleagues wants her to lead them into another election. She knows that the only debate among Tories is when, not if, they will tell her to go.

Credible sources say that she very nearly quit on 9 June and was only persuaded not to announce her departure there and then when it was pointed out that this could have led to a situation where the Queen was obliged to invite Jeremy Corbyn to Buckingham Palace to give him first go at trying to form a government. Mrs May recently admitted that she shed “a little tear” when she realised how monumentally she had fouled up. That only hints at the soul-scorching sense of personal failure, rejection and humiliation that she feels at having squandered a massive advantage and thrown away what was supposed to be an unlosable election.

I hear that she has told her closest friends that the election result was the most devastating thing to have happened in her life since the deaths of her parents when she was in her 20s. Mrs May’s inability, even a month on, to give a coherent explanation of why she thinks the election went so horribly wrong for her suggests that she has yet to process the trauma fully.

She knows that her colleagues regard her as a shattered leader. Whenever she is in the company of foreign leaders, she must also be aware that her international peer group think of her as a lame duck. It is never easy being a prime minister in a hung parliament. It has to be even harder when you have a personality that is terrified by the idea of not being in control. Some of her allies in the Cabinet – she still has a few – talk optimistically about Mrs May finding a way to reinvent herself and returning from the summer break with a plan to rebuild her credibility.

The immensity of that challenge was underlined by the reaction to the speech she delivered last week to mark her first year at Number 10. The speech was trailed as “a relaunch”. Unwisely so. Leaders who “relaunch” usually do so because they are sunk. The most notable feature was her plea to the opposition parties to “contribute, not just criticise” and “to come forward with your own views and ideas”. In a different context, this appeal might have won plaudits for being attractively unpartisan, but it was a month too late. The right day to have extended the olive branch and talk about fashioning a consensus would have been 9 June. The appeal would very probably have been scorned, but it would have come over as more bold and authentic had Mrs May acknowledged her changed status in the immediate aftermath of the election. To wait five weeks and then suggest that she is up for some inter-party co-operation reeks of desperation and was inevitably interpreted as further evidence of her debilitation.

If Britain were more like Germany, there would likely be “a grand coalition” to navigate the perilous waters ahead. But if Britain were more like Germany, Brexit would not be happening in the first place. The Labour leadership has neither the inclination nor the incentive to work with Mrs May and she lacks the strength or dexterity to make the opposition look bad for spurning her offer. Labour and the other opposition parties don’t regard the Brexit legislation as a reason to throw a life preserver to the government. For them, it is an opportunity to make the seas hellishly rough for the Conservatives.

I recently asked a member of the cabinet what Mrs May could possibly do. She laughed and replied: “KBO: Keep Buggering On.” As a motto for government, this lacks inspiration, but it sounds entirely realistic in its poverty of ambition. I asked another member of the cabinet, one of the few ministers who is genuinely close to Mrs May, whether there was anything that could change the narrative of doom around her premiership. His remedy was “time”. This minister mused that there might be some event over the horizon, an unforeseen crisis that, if handled right, could offer Mrs May the opportunity of a second audition with the country.

I suppose we should never say never. We do live in incredibly volatile times; public opinion can be extraordinarily fickle. Ask Jeremy Corbyn. Not so long ago, the Labour leader was plumbing record depths for unpopularity; now, senior Tories tell me that Mr Corbyn would become prime minister if there was an election tomorrow.

History provides some examples of prime ministers who have been rescued from apparently irretrievable positions. In the summer of 2008, Gordon Brown looked done for. Virtually all the media had turned on him. The public couldn’t stand him. Key colleagues were preparing to oust him. Then along came the Great Crash, to which Mr Brown reacted with a decisiveness and vision that had been hitherto absent from his premiership. He was acclaimed, at home and abroad, for having the right skill set for that crisis. His approval ratings bounced. Plotting against him evaporated. His self-belief was restored. That recovery didn’t last. He went on to lose the subsequent election, but Mr Brown did manage to buy himself some extra time at Number 10.

Mrs May is still in office because her party fears what it might do to itself in a chaotic and vicious Tory leadership contest. There is no widely agreed candidate to replace her as prime minister. There is no name that could be put to the cabinet and receive overwhelming support as the next occupant of Number 10.

Which brings me to one final word about the Shelburne premiership. Soon after he was ejected from Number 10, in came William Pitt the Younger, one of the greats in the pantheon of premiers. Given the mess Britain has got into, we could do with a 21st-century incarnation of that leader who unified his country and restored its confidence. Unfortunately, here I have to say that I struggle to find any historical rhymes. Gaze upon the potential candidates to succeed Mrs May for as long as you like and you will find it hard to glimpse a Pitt the Younger for our times.