British Prime Minister Boris Johnson's Conservative Party lost control of traditional strongholds in London and suffered setbacks elsewhere in local elections, with voters punishing his government over a series of scandals.

As early results suggested Johnson, a former London mayor, was losing support in southeastern England, his supporters moved in quickly on Friday to say it was not time to oust a leader they said could still "get things done" to help the economy.

Johnson's party was ousted in Wandsworth, a low-tax Conservative stronghold since 1978, part of a trend in the British capital where voters used the elections to express anger over a cost-of-living crisis and fines imposed on the prime minister for breaking his own Covid-19 lockdown rules.

For the first time, the opposition Labour Party won the council of Westminster, a district where most government institutions are located. The Conservatives also lost control of the borough of Barnet, which has been held by the party in all but two elections since 1964.

"Fantastic result, absolutely fantastic. Believe you me, this is a big turning point for us from the depths of 2019 general election," said Labour leader Keir Starmer.

Johnson, speaking in west London, said it had been a "tough night" in some parts of the country and his government had heard the demands from people for more help with the cost of living.

"We've had a tough night in some parts of the country, but on the other hand, in other parts of the country, you're still seeing Conservatives going forward and making quite remarkable gains," he told reporters.

"The big lesson that I take from this is that this is a message from voters that what they want us to do ... is focus on the big issues that matter to them: taking the country forward, making sure that we fix the post-Covid economic aftershock."

Johnson became the first British leader in living memory to have broken the law while in power when he was fined last month for attending a birthday gathering in his office in 2020, breaking pandemic social distancing rules then in place. (Reuters)