Labour has called for Theresa May’s former communications director to be sacked from the BBC board over claims he tried to block someone from a senior job on political grounds.

Sir Robbie Gibb, who became non-executive director at the Corporation in May, tried to stop Jess Brammar, former HuffPost UK editor and Newsnight journalist, from becoming BBC executive news editor, according to the Financial Times.

Sir Robbie, a former senior BBC journalist, texted Fran Unsworth, BBC director for news and current affairs, saying the broadcaster “cannot make this appointment” because the government’s “fragile trust in the BBC will be shattered” if it did, the newspaper reported.

Deputy Labour leader Angela Rayner has written to BBC director general Tim Davie demanding Sir Robbie be removed from his position.

“If Robbie Gibb won’t resign then the chair of the BBC must sack him,” she wrote on Twitter.

Jo Stevens, shadow digital, culture, media and sport secretary, added: “These allegations raise very serious questions about Conservative cronyism at the heart of the BBC.

“If Robbie Gibb is in post to further Tory interests rather than the public interest, then he is in the wrong job.”

Ms Brammar had applied for a newly-created post that oversees BBC output on its UK and global news channels, according to the FT.

She used to work as deputy editor of BBC Newsnight and ran the HuffPost UK website until the company was bought by Buzzfeed, which made editorial staff redundant.

Sir Robbie now works as senior communications adviser at Kekst CNC and is director of the Jewish Chronicle, but served as Theresa May’s director of communications from 2017 to 2019.

The row comes at a time when Mr Davie has attempted to address concerns about the BBC’s impartiality.

The broadcaster said in a statement: “The BBC doesn’t comment on ongoing recruitment processes, which are the responsibility of the executive, but for the record, no recruitment process has been blocked.

“People should wait for the outcome which will be announced in due course.

“And as a general principle, board members are able to discuss issues with other board members or senior executives. These principles were adhered to.”