Labour leader Jeremy Corbyn has come under fire from some of his MPs after devastating losses for the party in Scotland - despite performing better than expected in England.
After overnight counts were completed, Labour had lost overall control of one council and a total of seven seats, while the Tories had gained nine seats and the Lib Dems had gained four.
Results from the remaining 46 councils are expected from 11am.
Batley and Spen MP Jo Cox said the results were "not good enough", while Bermondsey and Old Southwark MP Neil Coyle - who nominated Mr Corbyn for the leadership - said Labour was "moving away" from the possibility of being in power come 2020.
He blamed senior figures' "fixation" with "peripheral" issues such as unilateral nuclear disarmament for failing to attract voters.
After six years of a Conservative-led government, he said, Labour "shouldn't be losing seats, it's as simple as that."
And Labour peer Lord Peter Hain warned that Mr Corbyn had "not shown anything like an ability to... win the centre ground votes that we need to win a general election."
Labour leader hits out at a harmful "running commentary" in the media as he admits the party is not in a position to win the next election.
MPs say the results show that Jeremy Corbyn's brand of socialism isn't working - but he has done well enough to stave off a coup.
A Labour MP opposed to Jeremy Corbyn just texted me: he has until next year to prove he can win the General Election in 2020.