In a transcript dating to September 2020 Dame Angela McLean also appeared to call a scientist who was critical of lockdown measures, Professor Carl Heneghan, a "f***wit".
Dame Angela, who has been the government's chief scientific adviser since April 2023, was deputy in the role to Patrick Vallance during the 2020-21 pandemic.
Mr Sunak had been criticised for launching the Eat Out to Help Out scheme over the summer of 2020, which encouraged people to return to restaurants with subsidised meals.
At some points of the pandemic the Treasury and Mr Sunak were also seen as opposed to lockdown measures because of their perceived impact on the economy.
Ministers and scientists were also reportedly split on whether so-called "circuit-breaker" lockdowns should be introduced in late 2020 to stem the flow of rising cases.
The PM has since said he was "wrong to empower scientists" during the Covid-19 pandemic and claimed the economic "trade-offs" of lockdown were never properly considered.
The messages displayed at the inquiry hearing on Thursday refer to a chat between Dame McClean and scientist John Edmunds.
The transcript ironically begins with WhatsApp's standard warning that "Messages and calls are end-to-end encrypted. No one outside of this chat, not even WhatsApp, can read or listen to them."
The transcripts were released to the public inquiry.
The Covid-19 Inquiry was set up by Boris Johnson in May 2021, with a start date of Spring 2022. The inquiry aims to examine the UK response to the pandemic and to learn lessons for the future.
Asked if Mr Sunak accepted the characterisation, a No 10 spokesperson said: “We’re not providing a running commentary on the ongoing inquiry. We will let that take its course.”
This article was amended on 20 October 2023. It previously said that Dame Angela’s use of the term ‘f***wit’ referred to NHS medical director Steve Powis, but it is instead thought to be a reference to Prof Heneghan.
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