Nigel Farage has hailed Reform UK’s gains in Thursday’s elections as “unprecedented” and “the end of two-party politics”.

The party has taken control of 10 local councils, won two mayoral races and added a fifth MP to its ranks in the Runcorn and Helsby by-election now counting has been completed.

Many of these wins came at the expense of the Labour and Conservative parties, which have both sought to explain the results.

Prime Minister Sir Keir Starmer conceded that people were not yet feeling the benefits of a Labour government, while Conservative leader Kemi Badenoch pledged to make her party a “credible” alternative once again.

Farage claimed on Saturday: “In post-war Britain, no one has ever beaten both Labour and the Tories in a local election before.”

Writing in The Times, Sir Keir said the lesson learned from the elections was not that the country needed “ideological zealotry”.

“It’s that now is the time to crank up the pace on giving people the country they are crying out for,” he said.

But some within Labour have called on the prime minister to change direction, saying the decision to cut winter fuel payments to all but the poorest pensioners had put off voters.

Labour MP Rachael Maskell urged the government to ditch the cuts, telling BBC Breakfast: “We have got that mandate, I believe, as a party to look at how we can better redistribute wealth, as opposed to taking out of the pockets of the poorest.”

With the results all in, Badenoch apologised to the defeated Conservative councillors, saying: “I am going to make sure that we get ourselves back to the place where we are seen as the credible alternative to Labour.”

Writing in The Telegraph, she said: “I’m deeply sorry to see so many capable, hard-working Conservative councillors lose their seats. They didn’t deserve it – and they weren’t the reason we lost.”

Badenoch blamed the party’s 14 years in government and a “punishing” general election which had both “sapped morale and resources”.

She also reiterated her view that defending many local seats the party had gained in 2021, during a “vaccine bounce”, was a “tough ask”.

The results were worse than Conservatives had feared, with the party not only losing to Reform but also the Liberal Democrats.

It lost 674 council seats and control of all 16 authorities it was defending – but wrested the Cambridgeshire and Peterborough mayoralty from Labour.

Roger Gough, the former Conservative leader of Kent County Council, told BBC Radio 4’s Today programme that the party had a huge job to do.

“We are still under the shadow of what happened when we were in government,” he said. “That’s a shadow that was over us when we went to the national polls last year and it hasn’t lifted.”

He added: “There’s a genuine pressure between coming up with serious answers, which will in some cases take time, and establishing a credible position in the shorter term.

“Clearly that’s not happened so far, that’s why so many of us paid the price electorally over the last couple of days.”

Shadow chief treasury secretary Richard Fuller insisted that Badenoch would be the party’s leader in a year’s time.

He told Today the party “has to think deeply about policies that are going to work, make sure we’ve got the people to put them in place, then regain trust”.

Fuller said the Tories would not make a pact with Reform, adding Farage “has been very clear that he wants to destroy the Conservative Party”.

The Lib Dems were the other standout winners, gaining 163 seats and control of three councils. They seized Shropshire from the Tories and gained control of Oxfordshire and Cambridgeshire after both previously had no party in overall control.

They also became the biggest party in Hertfordshire, Wiltshire, Gloucestershire and Devon, where they narrowly fell short of an overall majority.

Lib Dem leader Sir Ed Davey said they had supplanted the Conservatives as the “party of Middle England”.

The party’s education spokesman, Munira Wilson, told the Today programme that the party was “standing up for British values both locally and nationally”.

She said: “It’s the party that will work on the issues that people care about, whether that’s the health and care services or fixing pot holes, or the party that will stand up for British interests on the world stage and will stand up to the likes of Donald Trump.”

The Green Party made some gains, winning 44 seats in total – however it suffered disappointment in the West of England mayoral race.

Green peer Baroness Jenny Jones told Radio 5Live the party had increased councillors every year over the past eight years.

“It seems an era of five party politics is happening and that’s very good for us, because as soon as people see it is not a choice between the Labour or Conservative, they start looking around for policies that suit them,” she said.

You can view the full election results here.