Kemi Badenoch has appointed the former policing minister Chris Philp as shadow home secretary and Alex Burghart as her de-facto deputy, as the new Conservative leader set out her full shadow cabinet.

However Tom Tugendhat, the former security minister who ran for the leadership, declined a role in the shadow cabinet although it was not immediately clear what he was offered.

The shadow cabinet’s first meeting will take place on Tuesday morning, which will have some continuity – including James Cartlidge as shadow defence secretary and Claire Coutinho, who had been tipped for a bigger promotion, as shadow energy and shadow equalities minister.

Ed Argar, a former health minister, will be shadow health secretary, Kevin Hollinrake will move from business to housing and communities and Victoria Atkins, the former health secretary, will shadow the Department for Environment, Food and Rural Affairs.

Burghart, a longtime supporter of Badenoch, will also be the shadow Northern Ireland secretary as well as shadow chancellor of the duchy of Lancaster, which is a de-facto deputy role.

Helen Whately will be shadow work and pensions secretary, Gareth Bacon shadow transport, Alan Mak the shadow science and technology secretary, and Stuart Andrew will be shadow culture minister.

Badenoch said the shadow cabinet “draws on the talents of people from across the Conservative party, based on meritocracy and with a breadth of experience and perspective, just as I promised during the campaign.

“Our party’s problems will only be solved with a team effort, and I am confident my shadow cabinet ministers will deliver effective opposition as we seek to win back the trust of the public.

“We will now get to work holding Labour to account and rebuilding our party based on Conservative principles and values. The process of renewing our great party has now begun.”

The appointments came amid some frustration that Robert Jenrick’s role as shadow justice secretary had leaked on Monday night when Badenoch had reportedly intended to announce only two key roles overnight – Mel Stride as shadow chancellor and Priti Patel as shadow foreign secretary.

Laura Trott was also announced on Monday as shadow education secretary, in order to respond to a parliamentary statement on the tuition fee rise.

There were also questions about whether Jenrick had initially sought another post, in a sign of potential tensions between the final two candidates to replace Rishi Sunak.

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On Monday morning, Nigel Huddleston, Badenoch’s new party chair, sparked further speculation over the pair’s relationship when he said reports that Jenrick was justice secretary had “jumped the gun”.

Jenrick has been a vociferous advocate of leaving the European convention on human rights (ECHR), whereas Badenoch has said that was not a “silver bullet” to solve illegal immigration. The shadow justice secretary post would give Jenrick responsibility for the party’s position on the ECHR – though any final policy decision would be up to Badenoch.

Badenoch had already appointed other loyalists to jobs, with Rebecca Harris becoming chief whip, and Huddleston being made Conservative party co-chair alongside Dominic Johnson, a Tory peer and former donor.

A number of senior Tories had ruled themselves out of frontbench roles. They included Jeremy Hunt, the former chancellor and shadow chancellor, and James Cleverly, the shadow home secretary, who was favourite to become the next leader until he was surprisingly removed in the final vote among Tory MPs.

Steve Barclay, the former health secretary and Brexit secretary, had also said he intended to return to the backbenches.