The correct reports in Sunday Times and Mail on Sunday this morning that some ministers (not all) want Theresa May to go now, and make way for a caretaker - either David Lidington or Michael Gove - tells me NOT she will definitely go within a few days (though she may) but that the Government is perilously close to collapse.

Because what it shows is the underlying split in the Cabinet between those ministers - Gauke, Clark, Rudd, Mundell - who want to stop a no-deal Brexit at any cost, and those who want to prevent either a referendum or a "soft" Brexit "in name only" - Leadsom, Mordaunt, Fox, Grayling - has become irreconcilable.

For a brief moment at the end of last week ministers on the more Remain side in particular thought replacing May would paper over this yawning gap on the most important decision this country has faced since we joined the EU in 1973 - but it can’t and won’t.

David Lidington is a contender for the PM's position. Credit: PA

In fact both of the contenders to replace her, Lidington and Gove, would hasten ministerial resignations, in that both would be as likely as May - in fact probably more likely - to steer the UK to a Brexit in which the UK would be seen by many Tories to be a "vassal" or subservient state, or even towards a people’s vote.

Ministers not in the Brexit ultra or Remain ultra camps are explicit with me that May’s imminent departure would solve nothing.

One said: "we need to play the ball not the man".

Another said: "no credible route from A to B" [ie from Cabinet unhappiness with her to finding a replacement who would unite rather than divide].

A third added: "I don’t believe it [May’s resignation] will happen and I would not be part of it. But everyone is turning over remote possibilities to try and get out of jail".

And there is the rub, the real importance of what is happening.

Environment secretary Michael Gove is also a contender to replace Mrs May at Number 10. Credit: PA

As I wrote last night, the coming few days will see MPs - not the government - forced to choose between a no-deal Brexit on April 12 and an alternative route they may select via the indicative votes on Tuesday and Wednesday.

The Prime Minister - whether May or Lidington or Gove - would in turn have to decide whether to negotiate MPs' preferred Brexit outcome with Brussels and the EU 27’s leaders.

If MPs were to coalesce around the two most likely options, either a Brexit in name only or a referendum, that would split both the Cabinet and the Tory party, right down the middle.

One minister said to me: "Let’s be clear, there will be some of my colleagues who will argue Parliament should be dissolved and we should take our chances in a general election rather than have a referendum or customs-union Brexit [a soft Brexit]".

European Union leaders pose for a group photo at an EU summit in Brussels. Credit: PA

This is why there is much talk of backbench MPs not just taking over the Brexit decision but the whole machinery of Government - by appointing someone trusted by all sides (as yet unidentified) from the backbenches as a Brexit caretaker PM in charge of a temporary government of national unity.

Will this revolt of the Commons against the PM and entire executive happen?

The mechanics of such a fully fledged coup are tricky.

But the looming decision on whether to leave the EU on 12 April is testing this minority Government to breaking point.

The unhappiness with May is a proxy for the failure of the entire Government to solve the most important and intractable problem of modern politics - a Brexit that does not destroy the institution that gave us the EU referendum, the Tory Party.

If May falls, the whole Government may well too.

Boris Johnson, David Davis and Damian Green all met with the Prime Minister on Sunday. Credit: PA

Update 1.10pm

Yet it already looks like the Cabinet coup against May is over before it even started.

Authoritative sources close to Gove tell me he does not believe there should be a caretaker prime minister - so it won't be him.

And David Lidington has said on the record he does not want to be PM...

The only outstanding question is whether May changes her mind and decides later today - having seen Boris Johnson, David Davis, Damian Green, et al, or the nearest the Tories have these days to the "men in grey suits" - that it would help her chances of getting her Brexit deal over the line to announce she would quit immediately after that deal is ratified by MPs.

One of those advising her says he thinks that if she promised to quit, that could swing the vote in her direction.

Others say any pledge from her to go would not make any difference at all.

As for her Cabinet colleagues, they think it is highly unlikely we'll hear from her on Sunday that she's going.

"It is simply not in her nature to give a date for her resignation" said one minister.

"But truthfully I don't know for sure."

Or to put it another way, the tradition of May's Cabinet ministers not having a clue what the PM will do on the big things that matter hasn't yet been broken, and probably will endure till that unknown date of her exit.

Some ministers fear a softer Brexit could lead to a General Election. Credit: PA

Update 1.29pm

As I said earlier, there is a good chance that in meaningful votes on Tuesday and Wednesday, MPs will back either a softer form of Brexit that breaches the PM's red lines - on ending freedom of movement and negotiating trade deal - or Kyle/Wilson referendum plan.

I have now asked eight members of the Cabinet whether they think May would respect the will of Parliament and negotiate either of those outcomes with the EU.

All said she would not.

"What then?" I asked.

All feared there would be a general election (which is also what Brexit Secretary Steve Barclay is mooting, as are Brexiter Tory MPs from the ERG) - which is what you'll remember I described as a very real risk earlier today.

You have been warned.

Yikes

David Lidington has said he has no ambitions of becoming a caretaker prime minister

Update 2.07pm

The point is that Lidington was some Cabinet ministers’ answer to the question “what do we do if MPs in indicative votes go for a soft Brexit that Theresa May will refuse to negotiate with the EU?”

They hoped he - as someone trusted by Labour - would take over for a few weeks to broker that compromise with Brussels.

Maybe it will still come to that, in preference to the chaos of a snap general election.

But truthfully with so many ministers and Tory MPs preferring an election to a soft Brexit, the cabinet probably won’t have the luxury of appointing a temporary caretaker PM.