The Conservatives shed more than 1,200 councillors, the deepest losses since 1995, while Labour failed to capitalise and lost more than 80 wards in council elections across England.
Both the main party leaders said voters had delivered a rebuke over the failure to agree a Brexit deal in a strong signal that cross-party talks could produce a compromise ahead of a deadline in the middle of next week.
The Prime Minister was confronted with anger from her own party, with backbench MPs calling for her removal and warning the party would be “toast” if it did not change direction.
While giving a speech at the Welsh Conservative conference, a heckler interrupted Mrs May saying: “Why don’t you resign? We don’t want you.”
Voters across the country vented frustrations over Brexit on both major parties. Conservatives lost control of 40 local authorities, with councils including Chelmsford, Winchester and Bath falling into the hands of the Lib Dems. Labour was also licking its wounds after forfeiting control in heartland councils like Burnley, Hartlepool and Bolsover.
Mrs May told the Welsh Conservatives in Llangollen: “I think there was a simple message from yesterday’s elections to both us and the Labour Party – ‘just get on and deliver Brexit’.”
Shadow chancellor John McDonnell tweeted: “So far, message from local elections – ‘Brexit – sort it’. Message received.”
And responding to the early results, Labour Party chairman Ian Lavery said: “We’ve got a clear message from a lot of these communities that the two main parties need to get on and get Brexit sorted.”
Talks between Labour and the Conservatives on a Brexit compromise deal will reach their climax next week, with time set aside for votes in the Commons on a possible agreement.
The government says the discussions must conclude by the middle of next week if European elections on 23 May are to be avoided.
SNP Westminster leader Ian Blackford warned it would be “unforgivable” for Jeremy Corbyn to “sign, seal and deliver a damaging Tory Brexit” with no option of a second EU referendum.
In Sunderland, which voted to leave the EU by 61 per cent, Labour held on to the council, but lost 12 wards, with the Liberal Democrats, Greens, Ukip and Tories all making gains.
Council leader Graham Miller said the party had paid the price for its stance on Brexit, with some MPs calling for a second referendum.
“The people of Sunderland have said ‘we are just not accepting that’,” he said. “We have seen a massive protest vote on that issue tonight.”
But that message was resisted by pro-Remain figures in Labour, with Houghton and Sunderland South MP Bridget Phillipson saying: “How does this narrative explain Labour losses to Lib Dems and Greens?
“Delivering a Brexit that will damage the lives of working people across our country would be a mistake of catastrophic proportions.”
After shadow cabinet member Barry Gardiner suggested the party was “bailing out” Tories in cross-party talks, Ilford North MP Wes Streeting warned: “Any deal – any – must go to a public vote.
“Without a commitment to a public vote, I’ll vote for a Labour-Tory deal when hell freezes over and I’m not alone in that.”
Polling expert Professor Sir John Curtice said voters were punishing both parties. “The Labour Party is losing where they are strong historically, the Conservatives are losing where they are strong historically,” he said. “It’s a plague on all your houses.”