The head of the influential Home Affairs Select Committee complained that Shami Chakrabarti has so far failed to provide clarity over questions on her peerage.

Keith Vaz, whose committee conducted a brief investigation into the rise of anti-Semitism, wrote to the former head of Liberty early this month to ask whether she was offered the honour before, during or after the conclusion of her own inquiry into anti-Semitism within Labour.

He further asked her to disclose the exact date the offer was made – but failed to get a response to that point.

Instead, Chakrabarti said only she “accepted” the honour after the publication of her report and insisted suggestions that her report was a “whitewash” were “deeply insulting and completely untrue”.

Clearly unimpressed, Vaz again wrote to Chakrabarti on 16 August. “I am sorry that the information you provided does not fully answer the question that was asked,” he wrote, in a terse letter published on the Select Committee’s website this week. “Answers would provide much-needed clarity to this issue.”

He gave her until 21 August to make clear when the idea of a peerage was first discussed with her, the date it was offered and when she accepted. However, the letter was only made public by the committee on 26 August, without any details of a further response from the peer to be. The home affairs select committee is due to release its report next month.

Jeremy Corbyn was among those giving evidence to the select committee’s probe, during which he insisted the Chakrabarti inquiry into anti-Semitism in the Labour Party was independent. Community leaders have said the timing of the peerage left the credibility of her report “in tatters”.

Labour leader Jeremy Corbyn nominated Chakrabarti for a peerage in David Cameron’s resignation honours list, in which the former prime minister put forward a number of Conservative Party donors.