End of May in June, new PM in August, Election in October?

The last days of May are here in more ways than one.

Today's agreement between Theresa May and senior Conservative backbenchers over her departure was intended to bring a degree of certainty.

Instead it's raised more questions and may not even get the Prime Minister through the two or three weeks' grace it was supposed to give her.

It's left MPs, including those within the government, asking what will be the point of the last-ditch, fourth attempt to get the Prime Minister's Brexit deal through parliament at the beginning of June.

She's agreed that, when the second reading of the Withdrawal Agreement Bill (still not actually published) is debated and voted on in that week, whether she wins it or loses it, she and senior backbenchers will start the process of selecting a new Conservative leader.

But nothing has changed in terms of parliamentary support for her deal. Why on earth would any opponents change their mind to vote for it in these circumstances? What on earth happens between the second reading and the other stages of a withdrawal agreement bill which increases the stakes considerably by being a bill rather than a motion as the previous three votes were. Why on earth are they doing it at all?

Does Theresa May continue to go through the motions of trying to get it through with a leadership election in progress? Or will she quit immediately after losing for a fourth time?

Politics has been bizarre until now but will be 'through the looking glass' then as an opposition source put it.

'It's just going through the motions,' said one Conservative about the bill.

Given all that, there are some who wonder if she'll even reach that point.

'She has no power now,' said one very loyal Conservative. 'She's just holding on and she shouldn't be anymore.There are those who want her to leave with dignity but you can't have that. Politics is a shit job and others kick you when you're down.'

The impatient might be disappointed. 'It won't be a rushed job,' one Conservative MP tells me. 'The party hierarchy will want everyone to feel that they've had their say and made contributions. It'll definitely be done by conference, probably before' but not squeezed into the weeks before summer recess.

Those who are pushing for a change at the top are pinning their hopes on a new leader having new momentum and new authority. That's why many want the next leader to be in place before the party's conference at the end of September. 'They'll have power then and will want to show it. They'll want to use the conference as a launchpad and 'airbrush out' the last two years,' as one MP put it.

Another Tory scoffed at 'the idea that Brussels will say 'ah, a new Prime Minister, that's just what we've been waiting for to change the withdrawal agreement. There's a strong chance the new leader will in the autumn be in the same place that we are now.'

All of which points to parliament finally giving up the ghost and admitting that it can't solve the Brexit problem it's set itself.

'We'll be looking at the choice between leaving without a deal and revoking Article 50 in October,' said one Labour MP.

But others, including Conservatives, think a General Election in October is the most likely outcome. Not that anyone expects it to solve anything.

What about the prospects of another referendum? The Welsh Brexit minister Jeremy Miles told the UK Brexit Secretary in a meeting on Thursday that the government should be preparing for one even if only as a contingency measure.

I spoke to a Conservative Brexiter who was beginning to change their mind about a confirmatory vote. It might not be the worst thing, they said but the question would be important. It would need to frame 'remain' as the disruptive option whereas in 2016 'leave' was seen as the disruptive option.

It would though, they said, add another 10 months to the process

So who might be the next leader be? One senior Welsh Tory told me that if Boris Johnson is on the ballot, he'll win.

It's a big if.

'I wouldn't bank on Boris getting on the ballot,' said another. He has a lot of opponents amongst Tory MPs who will try to make sure his name doesn't go to the membership vote.

Another senior Welsh Tory is willing to give Johnson a go. He reaches out beyond the party, they told me. And during his time as mayor he's proven he can do a serious job when he wants to.