Labour has gained key London councils from the Conservatives, with Tories suffering losses across England in local election results so far.
Labour leader Sir Keir Starmer said his party had reached a "turning point" and was "back on track" to succeed at the next general election.
There was criticism of Boris Johnson from some Conservative council leaders.
But the Tories said Labour lacked the "momentum" across the country needed to regain power after more than a decade.
The Lib Dems have enjoyed good results, gaining 59 councillors and taking Hull City Council from Labour.
With just under half the local election counts for England completed, the Tories are on track to lose about 250 council seats in total, according to polling expert Sir John Curtice.
The full results - as well as those for councils in Scotland and Wales and for the Northern Ireland Assembly - will be announced later on Friday and on Saturday.
Results so far include:
- Labour winning south London borough Wandsworth from the Tories, who have held it since 1978
- Labour taking Westminster, Barnet and Southampton councils from the Conservatives
- The Conservatives holding majorities with reduced seats on councils including those in northern England, as well as Redditch and Dudley
- Labour keeping control of councils with lower majorities, including Wolverhampton, Salford and Coventry, where its vote has been historically strong
- In a referendum, voters choosing to ditch Bristol's mayoral system and change the way the city council is run
Ahead of the elections, the Conservatives had been braced for big losses in England, as they faced attacks over the rising cost of living and the ongoing Partygate scandal, including the prime minister's fine for breaking lockdown rules.
Conservative Party co-chairman Oliver Dowden told BBC Breakfast voting had taken place against a "difficult backdrop" for the government, adding: "We've had some difficult results and we can see that in London."
But the outcome so far did not "demonstrate that Labour has the momentum to form the next government", he said.
Although Conservative losses are not as bad as some in the party had been warning, there was still criticism of Boris Johnson from his own side.
The Conservative leader of Carlisle City Council, John Mallinson, said the prime minister "bears a lot of the responsibility" for the results and was a "poor option" to lead the party into the next general election.
"I think if things remain the same, we'll pay for it," he told BBC Radio 4's Today programme, adding: "The cost-of-living crisis is weighing very heavily on people's minds, and I have to say that issues like Partygate made it increasingly difficult to focus people's minds on local issues."
Ravi Govindia, leader of the Wandsworth Conservatives, said: "Let's not be coy about it. Of course national issues were part of the dilemma people were facing."
And Conservative MP David Simmonds said Mr Johnson had "difficult questions" to answer, adding: "Overwhelmingly the message that I heard on the doorsteps was people were broadly positive about the government's policies, but they are not happy about what they have been hearing about Partygate."
Sir Keir visited Barnet, north London, on Friday to celebrate Labour taking the borough from the Conservatives, calling out to a crowd of supporters: "This is a big turning point... From the depths of the 2019 general election, we're back on track."
"We've sent a message to the prime minister: Britain deserves better," he added.
But analysis of key wards by Sir John Curtice suggests Labour's overall support is down by 0.2% since 2018, when most of the seats up for grabs this time were last contested - and the party recorded its best local election performance under the then leader, Jeremy Corbyn.
Liberal Democrat leader Sir Ed Davey told BBC Breakfast that results so far for his party - particularly taking Hull back from Labour after 11 years - were "very promising", adding: "There is now a real picture emerging across the country, particularly in areas held by the Conservatives, that the Lib Dems are the real challengers."
BBC
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