The opposition Labour Party's shadow education secretary Bridget Phillipson said on Wednesday that Suella Braverman was back as the UK Home Secretary as the result of a "grubby deal" which helped Rishi Sunak "get over the line and become Prime Minister".
Speaking to the BBC, she argued that this calls into question Sunak's pledge to run a government of integrity.
She added that the discussion "should be about the future of our country, not the future of the Conservative Party".
However, Phillipson gives a cautious welcome to the installation of Gillian Keegan as education secretary.
Keegan left school at 16 and served an apprenticeship.
Phillipson says that news is "wonderful", but went on to highlight a "massive drop-off in apprenticeship starts" and a "failure to prioritise skills" by Conservative-run governments.
On Tuesday, Sunak kicked off a row by reappointing the Indian-originBraverman as Home Secretary, just days after she quit over a technical breach of government rules.
Braverman, an outspoken critic of former Prime Minister Liz Truss's economic policy, stepped down last week after breaching email security rules.
In her resignation letter, she had also raised concerns about the direction of Truss's government.
Also on Wednesday, the Liberal Democrats called for a Cabinet Office probe into Braverman's re-appointment.
In a statement, Liberal Democrats home affairs spokesperson Alistair Carmichael said: "Suella Braverman's appointment makes a mockery of Rishi Sunak's claims to be bringing integrity to Number 10.
"There must be a full independent inquiry by the Cabinet Office into her appointment, including any promises (Prime Minister Rishi) Sunak made to her behind closed doors."
Carmichael added that Braverman should be sacked if it is confirmed she "repeatedly broke the ministerial code and threatened national security".
"A Home Secretary who broke the rules is not fit for a Home Office which keeps the rules."