The Conservatives could lose more than 800 seats in the local elections, according to predictions.
Here is all you need to know about Thursday’s polls.
Where are the local elections taking place?
Elections are being held in 248 English councils outside London, and 11 local authority areas in Northern Ireland.
There are also polls for six elected mayors in Bedford, Copeland, Leicester, Mansfield, Middlesbrough and the new North of Tyne devolved regional authority.
Polls open at 7am and close at 10pm. Counting will take place overnight in about 120 areas but will be carried out during the following day in others, with the last result not expected until about 9pm on Friday.
What does the picture currently look like?
Nearly 60% of the 8,425 seats up for grabs in England are currently Conservative, with a quarter held by Labour.
A majority of seats involved were last contested in 2015, at a point when the Conservatives were on an electoral high, securing their first House of Commons majority for 18 years on the same day.
Under David Cameron, the Tories comfortably topped the poll, gaining 32 councils and 541 councillors as Labour and the Liberal Democrats both slumped.
How are the parties likely to fare this time round?
In terms of council seats, the Conservatives are currently at a historic high for a governing party after nine years in power, making losses all but inevitable even if the Tories were not riven by disputes over Brexit.
Conservative peer and elections expert Lord Hayward has predicted the loss of 800 or more councillors for Mrs May’s party – around a sixth of the seats they are defending.
He predicts that Liberal Democrats will be the principal beneficiaries, gaining 500 or more seats to Labour’s 300. Any gains higher than this would be regarded as a big success for the two opposition parties.
Most of the electoral battles are in the Tory shires or Labour strongholds in northern cities, limiting the prospects for large-scale gains by Jeremy Corbyn’s party.
Will voters’ thoughts on how Brexit is panning out have much of an impact?
As well as local factors, the ongoing row over Brexit is expected to play a major role in the elections. Conservatives fear Leave-backing supporters will stay at home or switch to Ukip in anger at Mrs May’s failure to deliver Brexit on time on March 29.
Labour risks losing votes from the Remain backers who make up a majority of its supporters if it appears too lukewarm on a second referendum, but could suffer in Brexit-voting areas of the Midlands and the North if it is seen to oppose EU withdrawal.
Are there any councils in particular to watch?
In Dudley, Trafford and Derby, Labour could gain overall control, while in Swindon, Great Yarmouth, Redditch and St Albans, control could slip out of Tory hands. The Liberal Democrats are hoping to seize Winchester.
What happens next?
The polls will be swiftly followed by elections to the European Parliament on May 23 – unless the Prime Minister is able to ratify her Brexit deal in time to halt them.
However, local results may not be a good guide to the Euro-elections, as neither Nigel Farage’s Brexit Party nor the Remain-backing Change UK are fielding candidates on May 2.
Polls suggest the European elections may be treated as a proxy second referendum by many voters, with Tories currently trailing in third place behind the Brexit Party and Labour.