The Conservatives have lost 1,334 councillors, with Theresa May saying voters wanted the main parties to "get on" with Brexit.
Labour also lost 82 seats in the English local elections, in which it had been expected to make gains.
But the strongly pro-EU Lib Dems gained 703 seats, with leader Sir Vince Cable calling every vote received "a vote for stopping Brexit".
The Greens and independents also made gains, as UKIP lost seats.
All 248 English councils holding elections have now announced their full results.
While the scale of the Conservative election losses is larger than expected, Labour had predicted it would gain seats, having suffered losses the last time these council seats were contested, in 2015.
The Green Party has added 194 councillors, while the number of independent councillors has risen by 612.
UKIP, which enjoyed large gains in 2015, lost 145 seats.
Results from Northern Ireland's 11 councils are also being announced. No local elections are taking place in Scotland and Wales.
After nine years in government it's not surprising that the Conservatives have lost a significant chunk of seats.
But the sheer number that have disappeared and the loss of control of authorities will hurt - especially with so many activists identifying Theresa May's handling of Brexit as a root of the problem, not just a general malaise.
The perceived personal nature of the failure is more of an indignity than an encounter with a heckler in tweeds.
And for Jeremy Corbyn, it is surprising and disappointing that Labour has simply failed to make any significant capital from such a divided and chaotic government.
However ardently his devotees swear loyalty, the party has fallen back - on this set of results at least - seeming further, rather than closer, from winning power in a general election he so often claims to crave.
MPs have yet to agree on a deal for leaving the European Union, and, as a result, the deadline of Brexit has been pushed back from 29 March to 31 October.
While local elections give voters the chance to choose the decision-makers who affect their communities, the national issue has loomed large on the doorstep.
Mrs May, appearing at the Welsh Conservative conference, said voters had sent the "simple message" that her party and Labour had to "get on" with delivering Brexit.
"These were always going to be difficult elections for us," the prime minister added, "and there were some challenging results for us last night, but it was a bad night for Labour, too."
A heckler shouted at the prime minister: "Why don't you resign?" He was then ushered out of the conference hall in Llangollen, North Wales, as the audience chanted: "Out, out, out."
BBC political correspondent Iain Watson said that while the Conservatives had lost "more than 10 times as many councillors", it was "remarkable" that Labour, "around the mid-term of a not-very-popular government - has not made net gains".
Speaking in Greater Manchester, Labour leader Jeremy Corbyn said he "wanted to do better" and conceded voters who disagreed with its backing for Brexit had deserted the party.
But Lib Dem leader Sir Vince, attending a rally in Chelmsford, Essex, where his party took control of the council, said it had been a "brilliant" result and that "every vote for the Liberal Democrats was a vote for stopping Brexit".
The BBC projects that, if the local election results it analysed were replicated across Britain, both the Conservatives and Labour would get 28% of the total vote.
The data, based on 650 wards in which detailed voting figures were collected, suggests the Lib Dems would get 19% and other parties and independents 25%.
Councils controlled per party (change since 2015)
- Conservatives: 93 (-44)
- Labour: 60 (-6)
- Lib Dem: 18 (+10)
- Independent: 2 (+2)
- Residents' associations: 2 (+1)
- No overall control: 73 (+37)
Polling expert Prof Sir John Curtice said the days of the Conservatives and Labour dominating the electoral landscape, as happened in the 2017 election when they won 80% of the vote between them, "may be over".
He said it was only the second time in history that the two main parties' projected national share of the vote had fallen below 30%.
The only other occasion was in 2013, when UKIP performed strongly in local elections.
Prof Curtice also said the Conservatives and Labour had both lost ground since last year's local elections when both were estimated to be on 35%.
While the Lib Dem figure was the highest since 2010, when they agreed to join the coalition government with the Conservatives, he said it was still well below the 24% the party regularly achieved in the 1990s and 2000s.
Green Party co-leader Sian Berry told the BBC the Greens were not simply benefiting from a protest vote over Brexit - their gains reflected "huge new concerns" about climate change as well as the strength of their local campaigning on a range of issues.
For UKIP, Lawrence Webb, a former London mayoral candidate who is standing in this month's European elections, said the party's "fortunes were on the up", despite the fall in its number of councillors.
This is the biggest set of local elections in England's four-year electoral cycle, with more than 8,400 seats being contested. A further 462 seats are up for grabs in Northern Ireland.
Six mayoral elections have also taken place, with Labour's Jamie Driscoll winning the contest to become the first ever North of Tyne mayor.
Labour candidates also won in Leicester and Mansfield but the party out lost to independents in Middlesbrough and Copeland.
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