You know things have not gone well for a Conservative leader when the Tory papers call, asking for pieces entitled "Was that the worst car crash speech of all time?"

Even allowing for the fact that some of these papers are engaged in the new Westminster game of "get her out and get Johnson in", it was certainly one of the most excruciating viewing and listening experiences of modern times.

At least when Tony Blair was slow-clapped by the Women's Institute, which was probably the most excruciating speech of my time working for him (though the time an audience member collapsed and emptied his bowels was a close second) there was a grotesque comic element to the whole thing. There was no comedy with Mrs May, not even when a comedian got involved. It was horrible. Even the most tribal Labour friends were telling each other "this is just tragic... I can't watch any more".

Of course we can all catch a cold, we can all have a bad cough, we can all get a frog stuck in our throat though – French stereotype joke alert – perhaps this will happen less once we're divorced from the EU. But as she soldiered on, the Prime Ministerial cough became a horrible ghastly metaphor for her, for her party, for her conference, for our politics, for Brexit, for Britain. 'The sick man of Europe,' someone tweeted. Someone else put out the image of Malcolm Tucker backstage screaming that they needed to fire a gun loaded with horse medicine into the Prime Ministerial bum.

The major cough was some time away when I first spotted, and tweeted, that she had a touch of the IDS cough problem creeping in. As the speech went on, all too little substance penetrating the well-worn lines that formed the basic construct, I was about to tap in 'the quiet woman is turning down the volume,' when I realised we were witnessing something that risked going from mildly irritating cough to full-on medical speech demolition.

Colds and conferences are natural bedfellows. The seasons are changing. All those germs. All that air conditioning. All those people bringing all their sniffles from their various parts of the world. All those late nights on crap finger food and copycat champagne. All that halitosis (experience from my journalism days tells me the Tories were usually the worst offender on that front).

So nobody should be surprised if ministers and even Prime Ministers catch something unpleasant. The surprise for me was that she was so medically uncared for. As an asthmatic I get more than my fair share of colds and chest infections, and am on antibiotics right now for a particularly unpleasant sinus explosion. But if you lead a life where public speaking is involved you have to find ways of getting yourself up at least for the time you're speaking. More than once I can remember Tony Blair having to be drugged up against cold and flu when making a big speech. He went through most of the 2005 election campaign with a slipped disc, which required regular treatment just to get him through an interview.

Twitters hilarious reaction to Theresa May's horror speech Wochit

So it can be done – and it has to be done – because in the main people are not terribly sympathetic to other people's colds and coughs. The same goes for bunged-up newsreaders and political hacks. Get them off-air and give us someone who can enunciate without sounding like they've got a frog in their nose as well as their throat.

Mrs May evidently doesn't have the best strategists, speech writers, spin doctors or conference set plasterers. But surely she could have found a decent doctor across the north west.

It was not as if we hadn't noticed she was not in great shape. She looked exhausted the minute she arrived in Manchester. The bags under the eyes have grown under the weight of Boris Johnson's Trump-sized ego and the irreconcilable impossibilities of Brexit. In her round of interviews yesterday the voice was beginning to croak.

I did have sympathy at that point. I know what a nightmare these big set piece speeches are, and thanks to Johnson and Brexit this one mattered more than most. So facing the inevitable late-night honing and the early morning polishing and practising will have made her feel even worse than she already did.

But here the sympathy ends. Because the cold and the cough are symptoms of a much deeper problem. She is doing a job she cannot do. And trying to manage a task that frankly nobody can manage.

Theresa May conference letters
The Conservative Party slogan was in tatters after May's speech Hannah McKay/Reuters

"Britain is leaving the European Union in March 2019." It was the single most important line in the speech. And it is the reason why she, her party, politics and the country in general are in a growing mess.

I totally accept that she became Prime Minister on the back of the EU referendum that led to David Cameron's demise and her elevation to the top job in the country. I also understand that she feels a sense of duty to deliver Brexit. And also that having launched and morally lost in the election campaign for which she apologised yesterday, she feels duty-bound to lead the government through the even more difficult minefield she helped to lay.

But the torture that we have seen on her face all week stems, in my view, less from the understandable irritation with the liar and charlatan she was daft enough to make Foreign Secretary than from her realisation – having looked at the issues every which way – that the reason Brexit is proving so difficult is because it is impossible to deliver in the timescale set out and with the maintenance of the promises made about it.

For the deluded ideological Brextremists and the dwindling membership of the Boris Johnson fan club, these questions lose them no sleep, any more than they lost sleep over the lies they told, the promises they made knowing they couldn't be delivered, or the questions they wouldn't answer because there was no answer to them.

I think Mrs May, by contrast, does at least try to think these questions through and is realising that she can't.

It is being said this has been the flattest and the most incompetently managed conference in living memory. Maybe. But there are two speeches that could and should have been made that would have electrified the place, set the political debate alive, and given Mrs May the outside chance of saving her Premiership, albeit with a huge risk.

The first speech should have come from David Cameron. He, not she, is the one who should have been up there making an apology. For holding a referendum and then losing it. For setting up his negotiations with the EU as the yardstick by which he should be judged. For using the referendum as a tactic to shut up Ukip and what Ken Clarke calls the Tory headbangers rather than putting in the intellectual hard work of a strategy for Britain in Europe. For failing to foresee that the consequences of the global crash meant any government that tried to make claims for a rip-roaring economy was going to take a kicking in a Yes/No binary choice. For then escaping to his shed and leaving the mess to someone else.

Simon Brodkin Boris Johnson Lee Nelson
Comedian Simon Brodkin aka Lee Nelson gives the thumbs up to Foreign Secretary Boris Johnson Christopher Furlong/Getty Images

Apology done, he should have then explained that though the people have spoken he hopes, as the cost and chaos of Brexit become clear, the people might at some point think again.

Then Mrs May could have made a superb speech in four parts. First, setting out why she backed Remain, but then explaining the things about Europe that irked her and therefore made her somewhat of a soft Remainer who failed fully to back Cameron and George Osborne. Third, explaining her sense of duty to deliver Brexit and the attempts she has made to do so. And then saying what she thinks and what she knows to be true – that this is Mission Impossible without enormous damage to the country, its economy, public services, culture, society and place in the world. And therefore she is going to revoke Article 50 and ask first Parliament, then the country to think again.

Cue howls of protest from some in the hall and possibly out on the streets. She would have to expect a challenge to her leadership and she might lose it. She would have to endure charges of betrayal wherever she went.

But it would give her a cause worth fighting for and show her to be doing what she believes to be the right thing. It would give her a confidence that seems to have drained from her bit by bit since she took over. It would give her a purpose.

Most importantly of all it might save the country from the decline into which Cameron has led us, and which she thus far seems hellbent on accelerating.

Even writing this I am alas fairly certain she will never do it. But I am totally certain that she should. Her cold, and much of the other weights she is carrying around with her, would suddenly feel an awful lot lighter.