“Après May, le deluge!” though Louis XV almost certainly never said it was, according to Marx in Das Kapital, “the watchword of every capitalist and every capitalist nation”. He was wrong about that, as he was about most things, but in the case of our current politics, it could be le May juste.

Take your pick of either the person or the month, because we’ve kicked off the latter with a set of election results from which we can conclude that the former’s Conservative Party is stuffed. And that Jeremy Corbyn’s Labour Party is stuffed, Ukip’s stuffed and Change UK is stuffed, while the LibDems, Greens, Independents and spoiled ballots have gone up, but not by enough, and nothing much has changed for the SNP.

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You may quibble that English council elections don’t offer many clues to the fortunes of the Scottish Nationalists, but if Boris Johnson can announce on Twitter that he’s cast his vote, only to delete the tweet after realising that there weren’t any elections in London, these are clearly piffling details when second-guessing the electorate.

In any case, the fact that the English counties, and some metropolitan areas, now hate both the main UK-wide parties has implications for the fortunes of the SNP in the European elections that – assuming they happen – will be on us like an uncast cloot before the month is out. And several guesses can be made about what local election results mean – even if no-one can ever offer a definitive verdict on the degree to which they predict voting intentions when it comes to returning MPs, MEPs or MSPs.

The Sage of Strathclyde, Professor Sir John Curtice, has already pointed out that the healthy total notched up by the LibDems and the Greens – though both parties will welcome it, and it has no doubt been bolstered by their opposition to Brexit – doesn’t at all signal a Remain backlash. Too many other factors, such as the support for Independents, the number of spoiled ballots and the number of people who simply didn’t vote, are just as much an indication of frustrated Leave supporters.

We can perhaps say with more confidence that the desertion of the Tories points in that direction, but it’s harder to say whether people who didn’t vote Labour didn’t do so because the party is insufficiently pro-Brexit, or not anti-Brexit enough. Or whether other factors, such as the ongoing anti-Semitism rows, or Mr Corbyn’s unpopularity with traditional, and Leave, Labour voters, play a major part.

There has been outrage from diehard Corbynistas at the idea that these results are bad for Labour, when the Tories have lost almost 1,300 seats, and Labour fewer than 100. Alas for them, that’s just confirmation of their basic trouble estimating support; going into the contest, the Tories held almost 5,000 seats, and Labour not many more than 2,000 that were up for grabs, because they were largely in Conservative areas, and the last poll was in 2015, when the Tories were doing well. They certainly did abysmally, but since Labour were hoping for gains of 500 seats or more, they’ve done pretty badly, too.

But all that hardly matters for predictive purposes. When it comes to Scotland, what the English elections tell us is that a great many of those naturally inclined to vote either Conservative or Labour are currently disinclined to do so. And who can blame them? The SNP are also fortunate in that those inclined to vote for any party robustly opposed to Brexit (which in Scotland, like London, also not voting this week, is the majority – unlike the rest of the country) won’t automatically defect to the LibDems or the Greens. For European Unionists, unless they are also staunch UK Unionists, a vote for the SNP does the job perfectly well.

This is a welcome fillip for the Nationalists, who might otherwise have expected to suffer from the disillusionment and fatigue that any governing party of long standing can expect. In other words, all the issues – falling school standards, inefficient bureaucracies, wasteful spending, failure to tackle NHS shortcomings, the usual scandals and cock-ups – for which every government, of any kind, gets blamed when it’s been in office long enough. The SNP already automatically attributes blame to Westminster or Unionist parties for such deficiencies, even when they are entirely devolved matters that they’ve had total control over for nearly a decade. But the fact that everyone is blaming the main UK parties, even in England, can only be a boost.

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The decline of Ukip south of the Border may have had more to do with the party’s own implosion and the fact that it was contesting very few seats; it would not be surprising if Nigel Farage’s Brexit Party did well there in the European elections. Again, that is not much of a hazard for the SNP, not just because Leavers are a minority in Scotland, but because they were likely already to have been in opposition to the Nats.

The confounding factor is this: the results of the English local elections are very bad for two people, Mrs May and Mr Corbyn; by which I mean personally bad for them, even more than for their parties. And both now have an incentive to agree on and push through a deal of some sort. Mrs May because she knows that, without even that Pyrrhic result, she will go down as an unmitigated, rather than merely a catastrophic, failure, and Mr Corbyn because most of his parliamentary party oppose his pro-Brexit stance and it is becoming apparent even to the dullest of his fans that, on the doorstep, his leadership is a toxic liability.

So there is, oddly, in this thoroughgoing indictment of both the leaders of the main UK-wide parties, an opportunity and an incentive for them to get something out of it for themselves; if they can do it fast enough, they could even theoretically avoid the electoral reckoning that will otherwise undoubtedly come at the end of the month. It would be a truly terrible sort of deal, offering something that Mrs May can deny is a customs union, and that Mr Corbyn can claim is, and that both Leavers and Remainers would loathe. That would be terrible for the country and their respective parties, of course, but they neither of them seem to care much about that.