Conservative leader Kemi Badenoch has rejected criticism of her leadership, saying anonymous critics from within her party are “cowards”.

“I’m not afraid of cowards,” she told BBC Newsnight.

Two anonymous Tories used an article in the Critic magazine to call for her to stand down, as the party braces for potential heavy losses in this Thursday’s local elections in England.

Badenoch said: “I’m not worried about people who are too scared to put their name to a piece of criticism.

“I think that’s cowardice,” she told Newsnight.

“I don’t know who would write anonymous articles or if it’s even real. But anything that doesn’t have someone’s name to it, I don’t think I need to worry about at all.”

The article, published in the magazine’s May issue and online last week, called for Badenoch to be replaced by shadow justice secretary Robert Jenrick – who she beat in last year’s leadership contest.

The article read: “Badenoch is not so much dragging the party down, as she’s where a party gets to when it reaches rock bottom.”

It described her as “unpopular and dislikeable and demonstrably no sort of electoral asset to the party”.

And it added that: “The Tory Party has not come to terms with its defeat last year, nor with the 14 years which preceded it… We are in massive trouble and are not solving our problems because we’re not admitting to them.”

Earlier this week, Badenoch rejected claims there was a rift between her and Jenrick over whether the party should form an electoral pact with Reform UK.

Badenoch also told Newsnight’s Nick Watt that she felt she was finding her “groove” as leader of the opposition, and was learning from the early experience of Margaret Thatcher who she said was “terrible at PMQs” at first.

“Leader of the opposition is completely different from being a secretary of state, which is what I did before,” she said.

“And you know, you find your groove, you try different things, some things work and some things don’t work.

“But what I’m really glad about is that my party is united. This time last year, what you would have been reading about in the papers was Tory rows, lots of infighting, and actually we’ve come together.”

Thursday’s polls are Badenoch’s first electoral test since she became leader, following her party’s defeat in last year’s general election.

The Tories currently hold about half the seats up for election on Thursday, and Badenoch has previously acknowledged they could be “extremely difficult” for her party.