Labour and the Tories have both lost control of key councils in the first wave of local election results.
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The Conservatives lost their only council in Greater Manchester in a defeat Labour claimed as a "huge coup".
Jeremy Corbyn's party, however, lost control of a Midlands councils in an area that is considered a bellwether seat at the general election.
Shadow chancellor John McDonnell and International Trade Secretary Liam Fox both said the results so far were "mixed".
The Conservatives lost Trafford Council after 14 years in power.
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Sir Graham Brady, chairman of the party's 1922 committee of backbenchers, told BBC News: "It's deeply disappointing for me and for a lot of Trafford residents."
Labour lost Nuneaton and Bedworth with the council falling to no overall control after the Conservatives gained seats.
The Conservatives gained Basildon and Peterborough, which had both been under no overall control.
Support for Ukip has collapsed with the party winning just two seats nearly five hours into counting.
Dr Fox told BBC News: "It looks as though the places where Ukip did well are reverting to their previous party."
London is the major battleground after recent polls pointed towards a substantial swing to Labour and the party believes it has a "fighting chance" in Barnet.
Liberal Democrats have gained a handful of seats in councils such as Liverpool, Hull and Portsmouth and are fighting to take Richmond upon Thames.
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Mr McDonnell played down suggestions the party could take Tory councils such as Wandsworth and said he believed it would be "really mixed" throughout the night.
"I don't think there are going to be big swings. What we are looking for is incremental gains that will lay the foundations."
Mayor of London Sadiq Khan, at the Wandsworth count, told the Press Association: "What I'd be disappointed by was if we didn't make progress across London in terms of the numbers of councillors.
Conservative former party chairman Grant Shapps, who has been highly critical of Prime Minister Theresa May's leadership, said No 10 and Tory headquarters had "got their act together".
He told BBC News: "Four years ago I was looking at a Conservative vote of 30% in the polls and today I expect Theresa May will be looking at significantly more than that, I imagine in the upper 30s, maybe near 40."
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Most councils are counting votes overnight but others will declare results during the day on Friday.
Across England, more than 4,000 seats are being contested in around 150 councils, including all 32 London boroughs, as well as every ward in Birmingham, Manchester, Leeds and Newcastle.
Mayoral elections are taking place in Hackney, Lewisham, Newham, Tower Hamlets, Watford and the Sheffield City region, but there are no polls in Scotland, Wales or Northern Ireland.
Voters in some areas piloting controversial ID trials were reportedly unable to cast their ballot.
Bromley, Gosport, Swindon, Watford and Woking councils have all trialled the scheme to help cut down voter fraud.
MPs and councillors said people, including elderly residents, were being turned away because they did not have appropriate ID.
Angela Wilkins, leader of the Labour group in Bromley, said five people have been unable to vote at polling stations as a result of the pilot and that the scheme is also causing long delays.
She tweeted: "Just been round the C Palace polling stations. 5 people not able to vote due to #voterID pilot and several walked away because of queues @CatSmithMP @labour4bromley. So why are we doing this .@LBBromley ?"
A Government spokesman said: "The overwhelming majority of people cast their vote without a problem."