Kemi Badenoch has admitted it is “feasible” that Nigel Farage could become the next prime minister.

The Tory leader told the BBC’s Sunday With Laura Kuenssberg programme Mr Farage’s party was “expressing the feeling of frustration that a lot of people around the country are feeling” – but added it was her job to “come up with answers and solutions”.

Asked if it was feasible that Mr Farage could be the next prime minister, she cited how Australian Prime Minister Anthony Albanese had won re-election this weekend.

“As I said, anything is feasible,” she said. “Anthony Albanese: people were writing him off. He has just won a landslide, but my job is to make sure that he [Farage] does not become prime minister because he does not have the answers to the problems the country is facing.”

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Asked what Mr Farage was doing right, Ms Badenoch said: “He is expressing the feeling of frustration that a lot of people around the country are feeling.

“But he also doesn’t have a record in government like the two main parties do. Now he’s going to be running some councils. We’ll see how that goes.”

Mr Farage was the undoubted winner of Thursday’s local elections, in which 23 councils were up for grabs.

His party picked up 677 council seats and took control of 10 councils.

By contrast, the Conservatives lost 677 council seats as well as control of 18 councils in what was their worst local elections performance on record.

Mr Farage said the outcome spelt the end of two-party politics and that his party was now the official “opposition” to Labour – with the Tories having been rendered a “waste of space”.

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Ms Badenoch said she believed the vote for Mr Farage on Thursday was partly down to “protest” but added: “That doesn’t mean we sit back. We are going to come out fighting.

“We are going to come out with the policies that people want to see, but what we are not going to do is rush out and tell the public things that are not true just so we can win votes.

“This is not about winning elections; this is about fixing our country. Yes, of course, you need to win elections to do that, but you also need a credible plan.”

Conservative co-chairman Nigel Huddleston sought to play down the threat from Reform UK, telling Sky News: “When they’re in a position of delivering things, that’s when the shine comes off.”

He told Sunday Morning with Trevor Phillips: “The one thing about Nigel Farage is, and we’re seeing this again and again and again, he is a populist.

“He is increasingly saying everything that anybody wants to hear. He’s trying to be all things to all men.”

“We are establishing ourselves as a credible alternative government based on sound conservative principles and values and our values and our principles, and therefore our policies, will define the future of our party,” he added.

Asked whether the results meant that Labour would now treat Reform as “your most serious opposition”, Health Secretary Wes Streeting told Trevor Phillips: ” I certainly do treat them as a serious opposition force.”

“As I say, I don’t know whether it will be Reform or the Conservatives that emerge as the main threat,” he added.

“I don’t have a horse in that race, but like alien versus predator, I don’t really want either one to win.”