Elections are held for 248 English councils, six mayors and all 11 councils in Northern Ireland
Conservatives and Labour both see vote shares fall compared with 2015
The Tories lose 44 councils and 1,334 seats
Theresa May says results message is: "Just get on and deliver Brexit."
Labour loses six councils and 82 seats
Lib Dems take control of 10 councils and won 703 seats
Greens and independents also make significant gains
Anger over Brexit appears to be influencing voters, say experts
Gerald Ramsden was elected after a dead heat in Hambleton.
This is the moment Gerald Ramsden is elected after a dead heat in Hambleton, North Yorkshire.
He was elected to the Northallerton South seat on Hambleton District Council after drawing with the Conservative candidate on 527 votes.
The returning officer had to randomly choose between two blank envelopes with one candidate's name in each.
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Tony Roe
BBC East Midlands political editor
Derby is currently home to a quarter of the country's UKIP councillors, as the party has lost 84 seats so far, leaving it with just 20 nationally.
Interestingly, two of them share a name, Alan Graves, because they are father and son.
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BBC political correspondent tweets...
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It's the 35th council that Conservatives have lost
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Conservative Party chairman Brandon Lewis says all MPs need to come together to address voters' frustration over Brexit.
“We are seeing around the country people showing that frustration with us, that in Parliament we have reached this kind of impasse," he tells the BBC.
“I think it’s a very clear message for both the key parties – us and Labour – that we’ve got to make sure we go forward and deliver on what people voted for in 2016."
“We want to see all of us as parliamentarians coming together, supporting the prime minister to get this deal done," he adds.