But a source close to her claimed they are automatically removed after a month – in a practice that pre-dates her application for the BBC position.
However, some of her old posts have re-emerged in recent days with many remaining visible on third-party websites.
In December 2019, in a tweet about a BBC interview with Mr Johnson, Miss Brammar listed ‘five things the Prime Minister said that aren’t true’ and in February urged people to ‘fight for a properly funded NHS’.
The posts, which have recently resurfaced, have reignited a recruitment row over concerns among BBC board members about her apparent bias
Some of Jess Brammar’s now-deleted tweets
Dec 2, 2019: ‘Whether you watched Boris Johnson’s interview yesterday or not, here are five things the Prime Minister said that aren’t true…’
Dec 10, 2019: ‘This piece on black Brits genuinely considering leaving the UK because of the level of racism, particularly if Boris Johnson wins, is really shocking… it won’t be a surprise to people who live this reality every day, and in admitting my shock I show my ignorance as a white woman.’
April 23, 2019: ‘Brexit: like Better Call Saul but less funny or interesting or enjoyable.’
Also in December that year she referred to an article by a colleague which said ‘black Brits’ were ‘genuinely considering leaving the UK because of the level of racism, particularly if Boris Johnson wins’.
Miss Brammar, who was previously deputy editor of Newsnight on BBC Two, then added that: ‘It won’t be a surprise to people who live this reality every day, and in admitting my shock I show my ignorance as a white woman.’
In April 2019, Ms Brammar tweeted that Brexit was like the Netflix drama Better Call Saul, about a shady lawyer, ‘but less funny or interesting or enjoyable’.
And, in January, Ms Brammar recommended a book by Sathnam Sanghera about British imperialism ‘to p*** off all the racists having a go at him’.
Despite her previous posts, Miss Brammar will be expected to uphold the BBC’s strict rules on impartiality should she be confirmed for the role.
But the intervention of Sir Robbie, who previously held senior BBC roles, earlier this month has reportedly already stalled the appointment.
He reportedly raised concerns about the way Miss Brammar handled a row with Treasury Minister Kemi Badenoch when she was UK editor of HuffPost.
A senior BBC News source recently told the Mail: ‘It’s a very unwelcome intervention – totally inappropriate and damaging.’
They claimed Miss Brammar was ‘still in play’ for the job. Labour has written to BBC bosses demanding Sir Robbie’s resignation.
Deputy party leader Angela Rayner wrote: ‘Putting pressure on the recruitment process of staff is entirely outside of the remit of the board and a total abuse of position.’ On Twitter she attacked ‘Tory cronyism at the heart of the BBC’.
However, a BBC spokesman stressed no process had been blocked, adding: ‘It is essential that board members can debate and discuss issues. They have an absolute right to do so. What individual board members can’t do is make decisions which are for the executive.’
Tory MP Julian Knight, chairman of the Digital, Culture, Media and Sport Committee, described the row as a ‘storm in a teacup’.
He said Sir Robbie, the brother of Conservative MP Nick Gibb, was ‘doing his job’ in letting the BBC know ‘where it should think politically in terms of what it does’.
He accused Labour of ‘politicising’ the situation.
MailOnline has contacted the BBC and Miss Brammar for comment.