Elections will be held for all 32 London boroughs, 34 metropolitan boroughs, 68 district and borough councils, and 17 unitary authorities, according to the Electoral Commission.
Voters will also choose the mayors of Hackney, Newham, Lewisham, Watford, and Tower Hamlets.
A parliamentary by-election in West Tyrone is also taking place.
The election is only being held in England, with 4,370 seats on about 150 councils on the line.
The previous vote was a snap parliamentary election held last June, a year after a referendum saw British voters decide to quit the European Union after 44 years of membership.
In that election, Prime Minister Theresa May suffered a partial defeat when her leading Conservative Party lost 13 seats as well as its parliamentary majority.
The Labour Party boosted its votes by almost 10 percent to win 32 extra seats in the House of Commons, and the Scottish Nationalist Party also lost 19 seats.
May had to agree on a deal with Northern Ireland’s Democratic Unionist Party (DUP) to maintain a majority in parliament.
Polling stations opened at 07:00 BST (06:00 GMT) and will close at 22:00 BST.
