The Conservatives won the West of England metro-mayor contest and gained control of five councils on an encouraging night for the Prime Minister.
Shadow chancellor John McDonnell acknowledged that Labour had suffered a "tough" night as it struggled in some of its Welsh heartlands and failed to resist Tory advances in England.
But he told ITV1's Good Morning Britain the results were not "the wipeout that people expected" and insisted it is still "all to play for" in the General Election in just five weeks' time.
Ukip suffered significant reverses, with voters switching to the Tories in a pattern which could provide a major boost to Mrs May as she hopes to strengthen her grip on power next month.
The Liberal Democrats were having a mixed election, failing to breakthrough against the Tories in the south-west England battleground.
Labour was dealt a severe blow in the south Wales valleys, with independents taking control of Blaenau Gwent and Merthyr Tydfil - where the final three seats will be declared on June 8 with Labour needing to win them all to regain a majority.
In Bridgend - the stronghold of First Minister and Welsh Labour leader Carwyn Jones - the party lost control
Mrs May had targeted Bridgend with a campaign visit in an effort to boost the Tory presence in Wales.
Things could get worse for Labour when counting begins in Scotland, with experts forecasting heavy losses for Mr Corbyn's party.
Shadow cabinet minister Barry Gardiner said it had been a "really disappointing night" for Labour but he insisted there were local reasons for some of the losses.
"In Bridgend, Blaenau Gwent and Merthyr I think it's right to say that most of the problems we have had there - losing control where we were in control - were through the splits within the Labour Party itself and the independents," he told BBC Radio 4.
Former Ukip leadership contender Lisa Duffy insisted the results had not been a "disaster" but acknowledged it was a "disappointing night so far, especially in Lincolnshire and Essex".
She told the BBC: "As a party we will learn from this, we will grow and we will move forward and we will continue to be positive."
Lib Dem president Baroness Brinton said the picture was "a bit patchy" for her party but "our areas of strength, we have done very well in, and I think that does bode well for the General Election".
Tory minister Brandon Lewis said Mrs May would "take the view that the results thus far are encouraging but there are still a lot of councils to declare".
"We can't assume that what happens in local elections will automatically be replicated in general elections," he told the BBC.
"There's a long way to go, there's a lot of work to do, we have got to work for every vote out there to make sure that we return Theresa May with a clear mandate on June 8."
In a sign of the problems facing Labour in England, a campaign visit to Harlow by Mr Corbyn the week before the vote failed to boost support in the Essex town, traditionally viewed as a bellwether seat, with the Tories winning a clean sweep on their way to retaining control in the county.
Mr Corbyn's party also lost ground in Cumbria.
While the county council remains under no overall control, the Conservatives replaced Labour as the biggest party, with the Tories effectively taking 10 seats from Labour.
Among those to lose their council seats was Labour's Gillian Troughton, who suffered a historic loss in the Copeland by-election to Conservative Trudy Harrison.
Ms Troughton is standing again to be Copeland's MP at next month's general election and will hope to avoid a hat-trick of defeats.
There was better news for Labour in Doncaster, where Ros Jones was re-elected as mayor after taking more than 50% of the vote in the first round.
In Warwickshire, the Tories gained control as Labour's representation collapsed from 22 to 10, while in Lincolnshire the Conservatives benefited from Ukip being wiped out.
Although the Lib Dems failed to prevent the Tories retaining Somerset, former Wells MP Tessa Munt defeated the Conservative council leader while in Eastleigh in Hampshire ex-MP Mike Thornton secured one of three gains from Ukip.
In the contests for new metro-mayors, Conservative Tim Bowles defeated Labour's Lesley Mansell in the run-off for the West of England post, covering Bristol and Bath.
After the redistribution of votes from candidates eliminated in the first round, Mr Bowles had 70,300 votes to Ms Mansell's 65,923.
Later today former Labour cabinet minister Andy Burnham hopes to begin life after Westminster by winning in Greater Manchester.
He is regarded as the favourite in the contest which will result in new decision-making and spending powers being in the hands of the winner.
A far more intriguing result is expected in the West Midlands, where two million people across Birmingham, Coventry, Sandwell, Dudley, Solihull, Walsall, and Wolverhampton will be eligible to cast a vote for the region's first directly-elected metropolitan mayor.
Former John Lewis boss Andy Street is running for the Conservatives while Sion Simon hopes to secure the role for Labour.
With full results declared by 17 of the 88 councils holding elections in England, Scotland and Wales, the Tories had control of nine authorities, including five gains.
Mrs May's party had 429 councillors, a net gain of 109, while Labour had 231, a net loss of 58.
Among the authorities which had declared their final results, Labour had control of two councils and had lost control of two.
The Lib Dems had 111 councillors, a net loss of nine; Plaid Cymru was on 40, a net gain of 10 and the Greens were on 10, a net gain of four.
Ukip had failed to win a single seat, a loss of 30.
Lib Dem former business secretary Sir Vince Cable called the night "neutral" for his party.
He said the party's overall vote share had increased significantly, while it had also made progress in areas like Cheltenham and Eastleigh, where it hoped to gain back MPs at next month's General Election.
"We're in a relatively encouraging position, though there hasn't been a spectacular breakthrough," he said.
Defence Secretary Sir Michael Fallon insisted the Tories were not complacent about the General Election despite the "encouraging progress" in the local contests.
"The reason we are not crowing is there is nothing yet, really, to crow about.
"Only a quarter of the votes have been counted and the turnout is only half what you get in a general election," he told ITV's Good Morning Britain.
"So it is far too early to predict - even from last night - what is going to happen by the end of today and it is five more weeks to the General Election."