The Liberal Democrats have suffered a bruising series of local election defeats, losing Cambridge council and dropping below 3,000 councillors for the first time in their history.
Nick Clegg's party was projected to take 16% of the vote - down eight points from four years ago.
It kept control of councils including Portsmouth and Watford but is expected to do badly in the London mayoral vote.
Former Lib Dem MP Lembit Opik has urged Nick Clegg to stand down as leader.
Mr Clegg said it had been "a disappointing and difficult night for the Liberal Democrats".
He added Labour had "clearly had a good night" but added: "I believe that over time people will come to acknowledge our unique role, the Liberal Democrats, in this government as the only party in British politics that combines responsibility on the economy with social fairness."
The Lib Dems retained control of Cheltenham, Eastleigh, Three Rivers, in Hertfordshire, and South Lakeland.
Lib Dem foreign minister Jeremy Browne said the party had "held up very well" where it had been running councils but it has lost 431 councils.
In London, Lib Dem mayoral candidate Brian Paddick finished a disappointing fourth.
Mr Opik told BBC radio 5live that Mr Clegg should stay as deputy prime minister but stand down as party leader.
He said: "My empirical view is that we would have done better with a different leader.
"I don't dislike Clegg as a person but I think you can actually point at specific mistakes he has made."
· All the latest election results are available at bbc.co.uk/vote2012