Liberal Democrat deputy leader Jo Swinson says that the election results were "amazing" and "beyond what we had hoped", with the party gaining 302 councillors and control of nine councils so far.

She tells BBC News that the result was particularly impressive as four-fifths of councils up for election were in areas that voted Leave in the EU referendum.

"We have a clarity and that clarity is respected. But it’s about much more than that. People look at their televisions in dismay at the wranglings between a government in disarray and from Labour not really in a better position," she says.

"All the while people want improvements to their lives - things are hard out there."

She says the result is a "springboard" for the European elections, but called for other Remain-supporting groups to work with the Liberal Democrats.

"To secure a people’s vote and stop Brexit we do need to work together," she says.

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BBC News Channel

Paul Scully, the Conservative Party's vice-chairman for London, denies that the local elections are a verdict on Theresa May as party leader.

"I think what it is is a verdict on Brexit as a whole and Parliament as a whole, almost a pox on all your houses," he says.

"If we start looking at leadership issues we’ve got a six-week window when the Conservative Party will just be speaking to itself just when then country wants it to speak to the country and get Brexit done."

He says the Liberal Democrat rise was down to a "protest vote" and blamed the loss of hundreds of "hard-working" Tory councillors on Westminster, where there are too many politicians "who are just interested in theory rather than pragmatism and what’s best for the country".

Liberal Democrat leader Sir Vince Cable tells BBC News that the results have been "spectacularly good, we've done massively well across the country".

Speaking from Chelmsford in Essex, where the party won 26 seats to win the council from the Conservatives, he says it represented "a recovery of morale from the difficult days several years ago".

"People are very dissatisfied with the Conservative government, the Labour Party are all over the place on the big issue of the day," he says.

"It has led to a situation where people are very fed up with the complete deadlock. Nothing is being done with the future of the health service and social care, underfunded schools, knife crime, homelessness, these are all being neglected."

But he says the result was also a "positive vote" for the Liberal Democrats.

Looking ahead to the European elections, he says: "We’ve seen from the evidence of tonight we are clearly the strongest of the Remain parties, and we expect that people will get behind us."

"People have been writing us off in the past, and I think we’ve demonstrated we are very much now part of three-party politics," says Sir Vince.

BBC News Channel

Green Party co-leader Jonathan Bartley says that the results have been "phenomenal".

The party has broken through on 16 new councils, "cementing our place as the fourth party in England in local government", he tells BBC News.

He rejects the suggestion that the party benefited from a protest vote, saying that it has made consistent gains in eight of the last nine elections.

"We know this is not just a flash in the pan," he says.

But he acknowledges the party gained votes from dissatisfied Remain supporters.

"It clearly is a Brexit backlash, it’s been very disappointing to see Labour’s equivocation, not backing a people’s vote, not being a Remain party," he says.

"With Greens you know what you're going to get."

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Liberal Democrat leader Sir Vince Cable says his party are "the big winners" of the local elections.

His party has already gained 300 seats - and control of eight councils.

Sir Vince says: "Voters have sent a clear message that they no longer have confidence in the Conservatives, but they are also refusing to reward Labour while the party prevaricates on the big issue of the day: Brexit."

He adds that the party has made gains in both Remain and Leave areas and the results are a "springboard to the European elections", where voting for the Liberal Democrats will be "a vote to stop Brexit".