May 5 is a big day for British democracy, with voters choosing the Scottish parliament, the national assemblies of Wales and Northern Ireland, four mayors including London, the London Assembly, Police and Crime Commissioners and thousands of English council seats.

The elections will be seen as a big test for all the main parties – and for Labour leader Jeremy Corbyn in particular – a year after the last general election.

If current polling is to be believed, the Conservatives are on course to embarrass Labour in the English council elections, Ukip could bag their first Welsh Assembly seats, and Labour’s Sadiq Khan will be the next Mayor of London.

These results may well be interpreted as a no-confidence vote in Jeremy Corbyn in England, a surge of support for Ukip in Wales, and a massive comeback for Labour in the capital. But none of these things is necessarily true.

Labour wipeout?

Polling expert Professor John Curtice of Strathclyde University has predicted that Labour could lose hundreds of English council seats.

Labour are behind the Conservatives in eight out of the last 10 major national voter intention polls.

Prof Curtice calculates that if Labour go into the election trailing the Tories by two points, they will lose 170 seats. If the two parties are level, Labour will shed around 120 seats.

That isn’t supposed to happen. Generally, it’s the ruling party that loses seats to the main challenger in the local polls that follow a general election:

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But the last couple of results have been unusual.

The local elections in 2011 – Ed Miliband’s first big test as the new Labour leader – were disappointing for Labour. They gained some seats, but not at the expense of the Conservatives, who also saw their share go up.

But Labour did exceptionally well in 2012, winning their biggest percentage share of councillors since 2003.

Prof Curtice told us Labour are now “defending a relatively high baseline” in the council elections.

He added that it is actually possible for Mr Corbyn to lose seats in England next week but still perform relatively better then Ed Miliband did when he was in the same position five years ago.

Reports suggest opponents of Mr Corbyn within the Labour party will want to use a poor result next week as a weapon against him, so it will be even more important to analyse the result carefully.

Mayor Sadiq?

Every major poll this year gives Sadiq Khan a significant lead over the Conservative candidate Zac Goldsmith.

Labour will take heart from a victory in the London mayoral election – but actually it shouldn’t come as a surprise.

Some analysts see the Conservative incumbent Boris Johnson’s last win as against the run of play, particularly since Labour won the London Assembly election on the same day with their best ever result in that contest.

Professor Steve Fisher from Oxford told us the polling reality is that “London is now a Labour city” and it was only the fact that the Conservatives had an unusually charismatic candidate in Boris Johnson last time that helped them buck that trend.

Ukip surge?

Ukip have been predicting a surge in Wales for some time now, but the experts are sceptical about what that really means.

Nigel Farage’s party were on 15 per cent in Wales, according to the latest Welsh Political Barometer poll, which puts them fourth behind Labour, Plaid Cymru and the Conservatives.

That is about the same as their popularity nationally – or a bit less. The most recent YouGov survey puts Ukip on 20 per cent across Great Britain.

If this were a general election, 15 per cent of the popular vote would not translate into many Westminster seats for Ukip, thanks to the “first past the post” system.

The party got nearly 13 per cent of the national vote last year and only ended up with one MP to show for it.

But Welsh Assembly elections are different. A third of the 60 members are chosen by proportional representation, so a decent showing for Ukip should result in several seats.

So it’s entirely possible that Ukip will win its first seats in Wales this time, but that won’t be evidence of a big surge in support nationally.