Polling stations for the vote - spanning metropolitan and district councils and unitary authorities - opened at 07:00 BST and will close at 22:00 BST.
There are no local elections in Scotland and Wales.
This is the biggest set of local elections in England's four-year electoral cycle, with more than 8,400 seats being contested.
A further 462 seats are up for grabs in Northern Ireland.
Voters in 10 local authorities in England will need to either show ID or produce their polling card before they can vote as part of a trial scheme.
Those in Braintree, Broxtowe, Craven, Derby, North Kesteven, Woking and Pendle will have to show ID before they can vote.
Voters in Mid Sussex, North West Leicestershire, and Watford local authorities will be required to show their polling card.
Everyone else in England will be able to vote as usual, and will not need to take their polling card or any proof of identity with them.
But in Northern Ireland, voters will need photo ID, the polling card received through the post being for information purposes only.
The weather forecast is for clear spells in the west and cloudier further east, with showers or more persistent rain.
Results for about 108 English councils are expected to be declared before 06:00 on Friday.
The remaining 140 are scheduled to come in throughout Friday, mostly between midday and 1800 BST.
The Northern Irish ones will take longer to come through because they have a more complicated voting system.
By-elections can take place in some council wards even if that council is not scheduled for elections this year. Check your council website for details.