One significant result saw the Tories retain control of Kensington and Chelsea despite anger over the response to the Grenfell Tower tragedy.
The Conservatives also gained Barnet, with Labour missing out on a key target council following its anti-Semitism row. The borough has a large Jewish community.
For UKIP, the highs of 2014 have turned into near obliteration, with the party losing 84 seats by 6.30am and retaining just two.
There were bright spots for Labour after 150 local authorities in England headed to the polls, but overall the party did not live up to expectations.
There was good news in Greater Manchester, where they became the largest party for the first time in 15 years – with the Tories losing overall control.
Labour also gained Plymouth, taking control from the Conservatives, but Mr Corbyn will come under pressure over disappointing results in the Midlands, with his party losing control of Derby and Nuneaton and Bedworth.
They also failed to take their target council of Walsall, which remained in no overall control.
There was plenty to cheer for the Lib Dems, who gained Richmond from the Tories amid signs of a Brexit backlash in a strong Remain-supporting area.
But overall Mrs May will be happy. There were gains in Peterborough and Basildon, the latter a result of capitalising on UKIP’s demise.
In London, the Tories also successfully defended Wandsworth and Westminster boroughs despite Labour hopes they could take both.
Meanwhile, Dudley remained in no overall control but the council’s Tory leader was confident a UKIP councillor and independent Conservative would join their group to hand them effective control.
With more than 100 of the 150 councils declared, the Tories were down one council overall, while Labour were unchanged.
The PM visited Wandsworth on Friday morning to congratulate local Tories for holding off the challenge of Labour.
She told cheering activists that the opposition “threw everything” at “one of their top targets” but failed.
Mrs May added: “We’ve seen other success in London. We’ve held Hillingdon, Barnet, Westminster.
“And outside of London, we’ve made progress in places like Dudley and Walsall. We’ve taken control in Basildon and Peterborough.
“And that’s all the result of the really hard work of our councillors, our activists, our supporters and our revitalised campaign machine.
“But we won’t take anything for granted. We will continue to work hard for local people and we will build on this success for the future.”
When asked by Sky News if the results showed Labour had passed the point of “peak Corbyn”, the Labour leader said:
“No, no, there is much more to come and it’s going to get even better.”
The Labour leader told Sky News: “We were defending seats that were last won in 2014, which was a particularly good year for Labour in local government.
“Obviously, I am disappointed at any places where we lost a bit of ground, but if you look at the overall picture, Labour gained a lot of seats across the whole country, we gained a lot of votes in places we never had those votes before.”
He added: “We are ready for a general election whenever it comes. A year ago, a general election was surprisingly called and we had the biggest swing to Labour for decades.
“We are absolutely ready for it. We have got members, we have got organisation, we have got enthusiasm.”
Counting is continuing throughout Friday, when mayoral results will also be declared.
Commenting on Tory fortunes, International Trade Secretary Liam Fox told Sky News: “It’s at the higher end of what we might have expected. It’s certainly a poor night in terms of the Labour Party outside London.”
More from Conservatives
Labour and Tories both lumbering like zombies after local elections
Cigarettes and tears as Labour count cost of anti-Semitism row
Conservatives hold Kensington and Chelsea despite Grenfell anger
Tory deputy chair James Cleverly denies party has Islamophobia problem
All you need to know about the local elections
HMRC raised Lycamobile’s Tory donations in denial of search warrant request
Speaking to Sky News, Labour shadow chancellor John McDonnell played down suggestions his party should have been enjoying a more dominant night.
He said: “All the hype in the media about Labour gains in certain boroughs was never going to be the case. What we were looking for was steady progress.”