Recent national opinion polls had shown Conservatives and Labour to be neck-and-neck on around 40% each.
Daily Star Online earlier reported the councils to watch for possible Conservative gains include Portsmouth, Basildon, Thurrock, Peterborough and Colchester, all of which could see the party win overall control on a relatively small swing. This was their biggest blow for the night, and understandably so in a predominantly Jewish area, with a nod to the Labour party's anti-Semitic problem.
In Northamptonshire, Labour may have snapped up seats from a weakened UKIP but the conservatives still claim overall control.
With 50 of 150 councils declared, all of them outside the capital, the Tories had gained two councils and 42 seats, with Labour losing eight seats and control of Nuneaton and Bedworth council, a key Midlands battleground.
The party would have still had a majority even if it had lost all of the seats it was defending.
Mr Khan, speaking at the Wandsworth count, told the Press Association: "What I'd be disappointed by was if we didn't make progress across London in terms of the numbers of councillors".
The Conservatives lost Trafford Council after 14 years in power.
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Sir Graham Brady, chairman of the Conservative 1922 committee of backbenchers, told BBC News: "It's deeply disappointing for me and for a lot of Trafford residents".
The election on Thursday, May 3, saw the Conservatives increase their majority on the authority from a one-seat to a five-seat majority.
"In part that is the result of the UKIP vote collapse and the Conservatives are advancing most strongly in Leave areas where Ukip were previously strongest".
Boys plotted to kill pupils and teachers in Columbine-style massacre at Yorkshire school, court toldMost councils are counting votes overnight but others will declare results during the day on Friday.
In Brompton and Hans Town, the ward of former Tory leader Nicholas Paget-Brown, who stood down in the aftermath of the fire, three Conservative councillors won seats.
Mayoral elections were held in Hackney, Lewisham, Newham, Tower Hamlets, Watford and the Sheffield City region.
In a message to the Grenfell community, he said: "Please put your trust in the enlarged and invigorated Labour group".