The Conservatives have lost control of key London councils in English local elections, but Labour has so far made fairly modest gains elsewhere.
The Lib Dems have made progress in Tory areas and took Hull City Council from Labour, in a good night for the party.
With just under half the results in, the Tories are on track to lose about 250 seats across England, according to polling expert Sir John Curtice.
The counts in Scotland, Wales and Northern Ireland get under way later.
The full results of those elections, as well those for mayoral contests, will come later on Friday and on Saturday.
