But the Tory Minister also said she would not give “specific examples of bias”, when she was questioned by MPs on the Culture, Media and Sport Committee.

It comes after Richard Sharp was forced to resign in April because he failed to disclose the role he played in getting then-prime minister Boris Johnson an £800,000 loan guarantee.

Dame Elan Closs Stephens has been appointed as interim chairwoman. She will take on the role on June 27 and remain in post until a permanent replacement is found.

Ms Frazer said the Government will appoint “the best person for the job” and there will be “a fair and open competition”.

“I will not be taking into account their political persuasions one way or the other,” she added.

John Nicolson, MP for Ochil and South Perthshire, said “it’s shoddy” that Mr Sharp – a former banker who had no experience in broadcasting – got “a plum public service job” after donating more than £400,000 to the Conservative Party.

He said people who make substantial donations to political parties should be barred from applying for the role in future.

Ms Frazer said: “It is inappropriate to disqualify people from public office because they happen to be interested in political life.”

She defended the former BBC chair, claiming he was “very knowledgeable” and he was held “in the highest regard” by colleagues.

A review by the BBC found there were “no concerns” about Mr Sharp’s integrity while he was chairman, but relevant declarations should have been made at the outset of his tenure, to avoid any conflicts of interest.

During the committee hearing, Ms Frazer said the BBC is an “institution that we should be proud of” but the broadcaster does not always provide “impartial news”.

“I’m not going to give any specific examples of bias, but I think there are often complaints about the BBC, some of which have been taken up by Ofcom and shown to be bias,” she said.

Last year Ofcom revealed that almost 40 per cent of the complaints made against the BBC involved claims about bias or misleading coverage and the broadcaster “needs to understand why this is the case and do more to address concerns”.

Tory MPs questioned the broadcaster’s impartiality in March after Match of the Day presenter Gary Lineker criticised the government's asylum policy on Twitter.

Ms Frazer also said the licence fee “isn’t the only way” to fund the BBC and the Government is looking at other models.

She later refused to be drawn on the Phillip Schofield scandal, claiming she is awaiting the outcome of a review commissioned by ITV. He resigned from This Morning last week after admitting that he had an “unwise but not illegal” affair with a younger colleague.

Culture Secretary Lucy Frazer claims BBC is bias but she cannot give ‘specific examples’