The Conservative Party needs to “stop acting like Labour” to win back power, leadership candidate Kemi Badenoch has said.

Launching her campaign with a speech in central London, the shadow communities secretary said one of her party’s mistakes in government was “we talked right but governed left”.

Calling for a smaller role for the state, she said government “should do fewer things, but what it does, it should do with brilliance”.

Ms Badenoch is one of six candidates fighting to be the next Tory leader, who will be announced on 2 November.

She has named her campaign Renewal 2030, arguing the Tories are unlikely to be in power again until the next decade so the focus needs to be on solving the problems of the future.

Ms Badenoch said that to win back the trust of the public the Tories “can’t just sit around pointing out how terrible Labour are” and “having the same policy arguments of the last Parliament”.

She blamed July’s historic election defeat on the public not knowing what the Tories stood for and delivering a “managerialist politics” which “wasn’t rooted in principles”.

She told a room of supporters and journalists that “a government that tries to do everything will likely end up achieving nothing”.

“This was one of our mistakes,” she said.

“We talked right but governed left, sounding like Conservatives but acting like Labour.”

The former business secretary pointed to the example of net zero targets to stop adding to the amount of greenhouse gases in the atmosphere, arguing that enshrining targets in legislation without working out how they would be met was “trusting regulation rather than innovation”.

On immigration, she said people “should not be made to feel guilty” for questioning the number of people coming into the country “if it is changing the place they know and love”.

Some of her leadership rivals, including Robert Jenrick and Tom Tugendhat, have called for a cap on legal migration.

However, Ms Badenoch said this would not solve the problem.

“We had a cap of tens of thousands when David Cameron came in,” she said.

“We need to ask ourselves why that didn’t work, rather than just saying we’ll make another promise.”

She also said she did not agree with Tories who were calling for the UK to leave the European Convention on Human Rights (ECHR), which sets out the rights and freedoms people are entitled to in signatory countries.

Critics, including Mr Jenrick, have argued the treaty limits the UK’s ability to deport asylum seekers and deter illegal migration.

But Ms Badenoch said leaving the ECHR “would not be enough”, pointing out that other countries who are signatories are able to deport the vast majority of people they want to.

“We’ve got to look at the whole system,” she added.

Ms Badenoch won support from some on the right of the party for being outspoken against “identity politics” in her previous role as minister for women and equalities.

However, she rejected criticism that she was more concerned with “culture wars” than the “bread and butter of opposition politics”.

“People who say that all I did was culture wars were not paying attention. I was doing my job,” she said.

“I was the equalities minister, I had to look after very, very tricky issues like race and gender – things that everybody ran away from. I didn’t run away.”

Meanwhile, shadow home secretary James Cleverly also launched his leadership campaign, calling for a “family-first society” rather than reliance on the state.

Shadow security minister Mr Tugendhat will launch his campaign on Tuesday, with other leadership rivals Mr Jenrick, Dame Priti Patel and Mel Stride making speeches and pitches in the media in recent days.

They are currently aiming to secure the backing of fellow Tory MPs, who will whittle the field down to four candidates in a series of votes by the time of the party’s annual conference at the end of September, before narrowing the field to two contenders.

Party members will then choose the winner from the final two, with the result announced on 2 November.