I haven't been following the Conservative party leadership election very closely (apart from the comic aspects such as the admissions of various people that they had used drugs but really hadn't enjoyed it - how about saying "Well I was out of my tree, it was great"). The reason is that it makes no difference to where we are or to the direction politics is taking, given that none of them is the kind of (rare) politician who makes the weather. The fact is nothing has changed since we got an extension from the EU and the underlying structural forces in UK politics are still grinding away.
The basic, unchanged, fact is that we have an electorate rapidly polarising between the two new political identities of Leaver and Remainer (with those two labels signifying one's location relative to the new aligning issue of nationalism versus cosmopolitanism, which means it isn't going to go away once Brexit is over). At the same time the parties we have reflect the old, economic division and so the division in Parliament does not match the division in the country. That means paralysis in Parliament and splits in both the main parties, which are both losing votes to the more pure Remain and Leave parties.
Some basic realities.
The EU is not going to renegotiate or change the deal on offer or alter the backstop no matter what. They would be prepared to move to something like a Norway deal but that is now not a political possibility here. I strongly suspect a lot of the EU governments have come round to Emanuel Macron's view that they are better off without us, having a no deal exit and taking any hit. It only takes one country to block any further extension.
Given that there will not be an extension after Halloween - unless it's to make time for either a GE or a second referendum.
There is a majority in Parliament against a no deal exit. There are about 30 Tory MPs, including several leading members of the cabinet, who have made it clear they would vote against their own party in a no confidence vote to stop one.
There is a majority in Parliament against a second referendum of the type being advocated. About 30 Labour MPs (at least) would vote against one, which is enough to block it. This remains the case even if the alternative is no deal, but that also isn't going to happen (see 3).
There was at one time a clear majority in Parliament for some kind of softer Brexit than May's deal (customs union or Norway, or Norway+). I expected this to emerge in the shape of a cross party coalition as the deadline approached. It didn't for two reasons. Firstly party loyalty was just a bit too strong, for both practical and sentimental reasons. Secondly (and more importantly imo) the Remainers in Parliament overplayed their hand. They were so determined to get a second referendum that they simply weren't prepared to support a soft Brexit - they continued to vote as though a no deal exit was their second choice. I think this will prove to have been a catastrophic error on their part. All irrelevant now though, those options are not viable any more because of the clear polarisation of the electorate. Meanwhile there is still an overwhelming majority against the only deal on offer from the EU (see 1).
That means that there are now only two possible outcomes: a no deal exit (currently slightly more likely) or a second referendum. The problem with the second option is that all of the pro-second referendum arguments are predicated on its being a choice between stay in and a deal. You can't do that if there's no deal passed. So the only way to get a second referendum will be to either have a three way choice with preferential transfer (deal - no deal - remain) or a straight choice between no deal and remain. I think that last option would be the right one but I very much doubt it will happen. The problem is the remainers are not flexible enough to do this - probably because they know that in such a scenario the outcome is too close to call.
If we did have a second referendum very hard to predict how it would work out although the most likely outcome would be a very narrow remain win. The point is that regardless of what happens about 40% of voters are going to be mad as hell. That will have all kinds of consequences going forward.
So actually the most likely thing to happen this autumn will be a General Election. That will be either very interesting or a total cluster fuck depending on how you look at it. With four parties having roughly even shares of the vote and serious splits in both Labour and Conservative parties, plus the SNP winning every singe seat in Scotland, I cannot see any high probability way that any party will get a majority. In fact I would bet on two elections this year. What that will do is sort out the new party alignment.