You probably know the headlines by now: the Conservatives have gained hundreds of seats in council elections in England, Scotland and Wales, mostly at the expense of Labour.

Ukip’s presence in local government has been pretty much wiped out, while the Lib Dem revival some people predicted failed to materialise.

Let’s dig a little deeper and find out what all this means for the General Election next month.

How bad is it for Labour?

The Shadow Chancellor, John McDonnell, has been putting a brave face on the results all day, describing them as “challenging” but not “the wipeout that some people predicted”.

It wasn’t clear whose predictions he was talking about.

Last month the eminent election experts, professors Colin Rallings and Michael Thrasher of the University of Plymouth, made their predictions for seat changes:

The local elections in England have actually gone a lot worse for Labour than Rallings and Thrasher predicted.

At time of writing, most but not all of the results have come in. The Conservatives have gained more than 300 seats and Labour are down 142.

The picture that is emerging is closer to the one predicted by Elections Etc, the forecasting site of Oxford Professor Stephen Fisher, who correctly saw much bigger gains for the Tories and a net loss of seats for the Lib Dems. (Prof Fisher’s site was also more accurate than many others in the 2015 General Election).

Is Jeremy Corbyn the problem?

Mr McDonnell said today that broadcasting rules could work in the Labour leader’s favour in the run-up to the vote on 8 June.

The shadow chancellor said: “As Jeremy gets more airtime, people will see the real Jeremy Corbyn emerge.”

We’ll have to wait and see whether the public will embrace Mr Corbyn in the coming weeks, but there is evidence that the Labour leader is currently much less popular than Theresa May or indeed his own party.

Pollsters YouGov ask panels of voters whether they have a favourable or unfavourable view of the main parties and their leaders.

Subtracting one from the other gives us a net favourability rating.

With the SNP, Lib Dems and Ukip, the party leaders are viewed about as favourably as their parties. But with Labour and the Tories, the story changes.

Theresa May is viewed much more favourably than the Conservative Party. The party has a net rating of -2 and Mrs May’s score is +10.

This fact does not appear to have been lost on the Prime Minister’s campaign team, who have splashed her name across posters while downplaying the Conservative brand.

YouGov respondents view Mr Corbyn much less favourably than the wider Labour Party. Labour’s net favourability is -27 and Mr Corbyn is on -42, more than 50 points lower than Theresa May.

Could there be a swing back to Labour?

Anything is possible, of course, but historical precedent is not on Labour’s side here.

As YouGov have pointed out, we have to back to 1983 and 1987 to find occasions when local elections took place around a month before a general election.

In both these elections, the Conservatives were in power, got the biggest share in the local polls and went on to extend their lead considerably in the national vote.

How do today’s results change the General Election forecasts?

Psephologists tend to warn against using local election results to predict what will happen in national polls.

Voters behave in different ways when they are choosing the next Prime Minister.

Turnout is generally much lower in council elections and they don’t take place over the whole country at the same time – Londoners did not vote this week, for example.

The BBC and Rallings and Thrasher try to come up with figures for what would have happened if there had been local elections everywhere, but these should not be confused with a forecast of what the general election result will be.

So most pundits will continue to focus on opinion polls which specifically ask people how they will vote on 8 June.

At time of writing, the last major poll (YouGov, 2-3 May) shows the Conservatives extending their lead over Labour to 19 points, which points to an emphatic Tory victory on 8 June.

The latest forecast from Electoral Calculus, based on a spread of recent polls, sees the Tories winning more than 400 seats, more than all the other parties combined. This would be the worst result for Labour since 1935:

There is always a margin of error around all these predictions, and most polling companies got the last general election result wrong.

This should be of little comfort for Labour supporters though: past polling errors have tended to underestimate real support for the Conservatives.

Are Ukip really finished?

While it may be wrong to assume that the general election vote will mirror the patterns that have emerged today, Ukip’s numbers in some general election voter intention polls have been dropping lately too.

And if the party managed to confound the pollsters and win a much higher share of the vote than current polling suggests, they have historically found it difficult to translate that support into Westminster seats.

Britain’s First Past the Post general election system always makes it harder for smaller parties to get MPs elected, and Ukip’s support has tended to be spread thinly geographically, rather than concentrated in the marginal constituencies where their candidates might win.

Lib Dem revival?

The council election results arguably were not as bad for Tim Farron’s party as they looked.

The Lib Dems lost seats but increased their projected national share of vote to 18 per cent from 15 per cent in 2016.

But remember that this number isn’t the same as a prediction of what will happen in June.

That’s why it’s probably unrealistic for Mr Farron to talk about the Lib Dems doubling their seats in Westminster based on the local results.

The party is still hovering at around 10 per cent in polls that ask people how they will vote in the next general election.

Electoral Calculus predicts that this level of support means the Lib Dems will fail to win any more parliamentary seats.