Millions of people will vote in local elections across England, Scotland, Wales and Northern Ireland on May 5, with some 2,700 seats to be filled and ballots for three city mayors and 41 police commissioners.

Most of the elections will be fought over local issues, but they will also be a test of popularity for the two biggest political parties, the Conservatives and Labour, and provide a barometer of the durability of the right-wing UK Independence Party.

The highest-profile election is in London, where the favourite, Labour's Sadiq Khan, could become the city's first Muslim mayor.

But in London, as in the rest of the country, turnout is expected to be low in elections for the mayor and a regional assembly, partly because many people are waiting to cast a more important vote in the referendum on June 23.

Previous elections for London's mayor since 2000 produced turnouts between 32 and 45 per cent, with this year's voter participation not expected to exceed that of the last election in 2012.

"British people don't like to vote too often," said Tony Travers, a political scientist at the London School of Economics.

"However interesting these elections are, there's no question that they are substantially overshadowed [by the referendum]," Travers said, adding that canvassers had told him some voters expected them to talk about the EU rather than local issues.

While the spotlight has fallen on divisions over a British EU exit, or Brexit, in Prime Minister David Cameron's Conservative Party in recent months, analysts say Labour faces the biggest threat in the English local elections.

The Labour Party is currently struggling with allegations of anti-Semitic sentiment among its ranks after two prominent members were suspended for making controversial remarks.

The party could lose up to 150 seats nationwide, although few councils are likely to switch control, according to forecasts by Colin Rallings and Michael Thrasher, who run the Elections Centre at the University of Plymouth.

Labour is most vulnerable in poorer northern areas where anti-EU and anti-migration sentiment is high, and voters want to discuss these issues ahead of the local elections, said Simon Hix, director of the LSE's Political Science and Political Economy Group.

"Labour politicians ... are very worried about fighting a strong Remain campaign [in the referendum]," Hix said.

"They themselves are very pro-European but they don't want to say that on the doorstep if there are lower-income voters who are worried about immigration and will come out and vote to leave, because UKIP, the next day, will be going on those doorsteps and saying: 'You voted against Labour for the first time in your life. You voted with us'."

Hix said this is "exactly what happened in Scotland with the SNP," referring to the Scottish National Party, which controls the Scottish Parliament, picking up disaffected Labour voters following a closely contested referendum on Scottish independence in 2014.

"This is why the local elections are really important, I think, for thinking about Labour strategy [for the referendum]," he said.

"Because if Labour has a meltdown in some of these local elections in parts of the north of England, then there will be even more pressure from these back-bench Labour MPs who are already worried about losing their seats in the next general election."

UKIP came third behind the Conservatives and Labour in a general election last May, winning 13 per cent of the vote but just one parliamentary seat under Britain's constituency-based system.

With UKIP's long campaign for Britain to leave the European Union about to reach its climax with the in-out referendum, analysts wonder if the party can maintain its appeal through party leader Nigel Farage's focus on immigration and his opposition to what he claims is a socio-political elite dominating British governance.

In Scotland, meanwhile, "the big question for these elections is whether the SNP is going to do even better and Labour even worse," Travers said.

As soon as the counts are over, or perhaps earlier, politicians on all sides will surge ahead with their campaigns for Leave or Remain in the EU referendum.

Writing for academic website The Conversation, Alistair Clark, a senior lecturer in politics at Newcastle University, said "given all the sound, fury and misinformation that is the contest for the EU referendum, people in England could be forgiven for not realizing that there are also local elections happening in early May."

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