The Conservatives have gained control of five councils and Labour have lost two in the first sets of results from local and mayoral elections.
Among Tory gains is Lincolnshire, where UKIP lost all of its seats in what one senior UKIP politician described as a “very disappointing” result.
Labour lost control of Blaenau Gwent and Bridgend.
Lib Dem results have been patchy and the party failed to stop the Tories retaining control in Somerset.
Many authorities, including all those in Scotland, will not begin counting until Friday morning.
A total of 4,851 council seats were up for grabs in 88 councils – all of those in Scotland and Wales and 34 in England – five weeks before the general election.
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At 07:00 BST, across the 21 English and Welsh counties that had fully declared results, the Tories had control of 10 authorities and 542 seats, a net gain of 147.
Labour had control of four authorities and 368 seats, a net loss of 119. The Lib Dems had 134 seats, a net loss of 24. UKIP had failed to win any seats, a net loss of 41, while the Greens had picked up five.
Professor of Politics John Curtice said that the Conservatives had so far put in their best election performance since at least 2008, with an average swing of seven points from Labour to the Tories since 2013.
He said the Conservatives appeared to have been the main beneficiaries of a sharp decline in support for UKIP.
The Conservative candidate for the new “metro mayor” post for the West of England, Tim Bowles, beat Labour’s Lesley Mansell by 51.6% to 48.4%.
Lib Dem president Sal Brinton described her party’s performance overall as “patchy”, while former business secretary Vince Cable said there had been no “spectacular breakthrough”.
Ros Jones, the Labour mayor of Doncaster, has been re-elected after getting just over 50% of votes.
Warwickshire, Lincolnshire, Gloucestershire, the Isle of Wight and Monmouthshire gained by the Conservatives, had all been under no overall control.
In Lincolnshire, where UKIP had 16 councillors elected in 2013, the party has lost all of its remaining seats.
Former UKIP leadership contender Lisa Duffy described that as “very disappointing” adding: “We knew it was going to be a difficult night.”
Labour has lost control of its Welsh heartland seat Blaenau Gwent to independents, and the result in Merthyr Tydfil is on a knife-edge as the final three seats will not be declared until 8 June and Labour would have to win them all to retain a majority.
Merthyr Tydfil’s Labour leader Brendan Toomey was among those to lose his seat.
He told BBC Radio 4: “It’s the birthplace of Labour, we are having a very disappointing evening to say the least.”
Analysis: Where the parties stand… so far
By Chris Mason
If the final result to be declared in these local elections, much, much later today, is the summit of the electoral mountain, this morning we are barely above sea level.
Flip flops on, we are still on the beach.
But for those of us up all night to witness the nocturnal arithmetic, clear trends began to emerge very quickly.
The Conservatives up.
Labour and UKIP down.
The Liberal Democrats patchy.
Vaughan Gething, a Labour member of the Welsh Parliament, said there was an “awful lot of work” for the party to do before the general election on 8 June.
He told Radio 4’s Today there had been “mixed messages” on the doorsteps about Jeremy Corbyn’s leadership, but there had also been strong results – with his party “turning back the Tory tide” to retain control of Newport and Swansea.
Wrexham and Flintshire councils have remained under no overall control, while the Conservatives saw off a challenge from the Lib Dems to hold on to Somerset County Council – although leader John Osman was ousted by Lib Dem former MP Tessa Munt.
Among battles to watch out for on Friday are the SNP’s attempt to seize control from Labour in Glasgow – and the Conservatives’ bid to take back overall control of Norfolk County Council.
For the first time, voters in Greater Manchester, the Liverpool City region, the West Midlands, Tees Valley, the West of England, and Cambridge and Peterborough will elect “metro mayors” covering combined local authority areas.
The mayors will mostly be responsible for economic development, but some will have powers over transport and housing.
Former Labour cabinet minister Andy Burnham, who is stepping down as an MP, hopes to become Greater Manchester’s first elected mayor while in the West Midlands, former John Lewis boss Andy Street is running for the Conservatives while Sion Simon hopes to secure the role for Labour.
This is a year of county council elections in England (34 councils, 2,370 seats). There were also polls in six unitary authorities where county councils and district councils have merged.
In Scotland, all 32 councils (1,227 seats) and all 22 councils in Wales (1,254 seats) were being contested.
In Doncaster and North Tyneside, residents voted for local authority mayors, who are elected leaders of their respective councils.
Local and mayoral elections: Conservatives make early gains}