Labour Party candidate Sadiq Khan appeared set to become London's first Muslim mayor as counting got under way following Thursday's elections for regional and local assemblies in England, Scotland, Wales and Northern Ireland.

Khan has 43 per cent of first preferences, with his main rival, Conservative Zac Goldsmith, on 32 per cent, according to a final YouGov survey for the London Evening Standard.

Taking account of second preferences, which are tallied if no candidate has more than 50 per cent of fist preferences, Khan led by 57 per cent to Goldsmith's 43 per cent.

"I'll be a mayor for all Londoners," Khan, a former human rights lawyer, said on Twitter after he voted on Thursday.

Millions of people voted in ballots for more than 2,700 seats on 124 local councils, three regional assemblies, several city mayors and 41 police commissioners.

The final count in the London mayoral election is expected early Frday evening, while most other results will be declared earlier Friday.

Most of the electioneering has focused on local issues but the polls in England and Wales are a test of popularity for the two biggest political parties, the Conservatives and Labour.

They could also provide a barometer of the durability of the right-wing UK Independence Party.

But turnout is likely to be even lower than usual for local elections, with forecasts of record low turnout for some elections in England, Wales and Northern Ireland.

Many voters appeared to be reluctant to head out to vote in May when they already expect to do so for a referendum on June 23 on whether the nation should remain part of the European Union.

Turnout was expected to be around 37 per cent in London's elections for the city mayor and members of a regional assembly.

Khan, the early favourite, remained on course to win this week despite a row after the Conservatives repeatedly highlighted his religious background and Conservative Prime Minister David Cameron claimed that Khan had associated with extremists.

Khan's campaign also survived a media focus on his party's infighting due to anti-Semitic remarks by two prominent Labour politicians.

Labour faces the biggest threat in the English local elections after gaining hundreds of seats in the last elections in 2012.

The main opposition 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.

The party appeared most vulnerable in poorer northern areas where anti-EU and anti-migration sentiment is high.​

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