The Labour party has lodged a formal complaint with the BBC over the treatment of the shadow home secretary, Diane Abbott, by the new Question Time presenter, Fiona Bruce during Thursday’s show.

Last week, Abbott accused the programme of legitimising racist abuse, claiming she was repeatedly interrupted and singled out before the show, with Bruce stepping in to correct her, wrongly, over the latest Labour polling figures.

Labour has also demanded to see footage from the audience warm-up before the show amid allegations the crowd in Derby had been “whipped up” against Abbott. She said she had also been told Bruce made unpleasant remarks about her before the recording began.

The BBC said it was “sorry” to hear of Abbott’s concerns and had sought to reassure her team that social media claims made about the warm-up, which have gone viral, were false.

“We are appalled by the treatment of Diane Abbott on BBC’s Question Time,” a spokesperson for the MP for Hackney North and Stoke Newington said. “It was clear that a hostile atmosphere was whipped up, propped up by reports of inappropriate and sexist commentary in the audience warm-up session.

“A public broadcaster like the BBC should be expected to be a model of impartiality and equality. The BBC cannot claim anything of the sort when analysis of the programme shows that the only black woman on the panel was jeered at and interrupted more times than any other panellist, including by the chair herself.

“The media must stop legitimising mistreatment, bias and abuse against Ms Abbott as a black woman in public life. The BBC should be ashamed that their programming is complicit in such behaviour.”

The BBC has acknowledged Abbott was right about the polling figures; however, Labour has said it wants an on-air apology. The shadow home secretary is a regular on Question Time, having appeared at least 29 times over several decades, according to her office.

A Labour source said: “We want to see the warm-up footage because of these claims from audience members and we want an on-air apology over the polling.”

Following Thursday’s Question Time and the criticism directed at the BBC, the corporation said in a post on Twitter: “We’ve reviewed what was said re polling on @bbcquestiontime. A YouGov poll published on the day of the programme suggested a lead for the Conservatives. Diane Abbott was also right that some other polls suggested Labour either as ahead or tied, & we should have made that clear.”

In a further statement, a BBC spokesman said: “Diane is a regular and important contributor to the programme.

“We firmly reject claims that any of the panel was treated unfairly either before or during the recording.”

In September 2017, it emerged that Abbott alone received almost half of all the abusive tweets sent to female MPs in the run-up to the general election, according to Amnesty International, much of which was racist and sexist.

Last month, the shadow home secretary said she experienced more racism now than at any time in her 35 years in politics.