The Culture Secretary has said she is “very pleased” that ITV has instructed a barrister to carry out an external review of the facts following Phillip Schofield’s departure from This Morning.

Lucy Frazer spoke to the Culture, Media and Sport Committee on Tuesday about a range of topics, including the departure of BBC chairman Richard Sharp and the Elgin Marbles.

Schofield, 61, resigned from ITV last month and was dropped by his talent agency YMU after admitting to an “unwise but not illegal” affair with a younger male colleague.

Ms Frazer said: “I think there’s an incident that’s happened. I’m very, very pleased that ITV are taking it seriously.

I look forward to understanding the detail of that review and the timing of that review and when I see that I will consider it very carefully

“I’m very pleased that they wrote to me, and to the committee, I’m very pleased that they’ve appointed a KC to investigate the position.”

Last week, the PA news agency revealed that Dame Carolyn McCall had written to Ms Frazer, DCMS Committee chair Dame Caroline Dinenage and Ofcom’s chief executive Dame Melanie Dawes.

The letter said ITV records show that “when rumours of a relationship between Phillip Schofield and an employee of ITV first began to circulate” that both parties “denied” it and this was reiterated “as recently as this month”.

It also said ITV has instructed Jane Mulcahy KC, of Blackstone Chambers, to “carry out an external review to establish the facts”.

On her response to Dame Carolyn, Ms Frazer said: “I wrote back to identify, and I look forward to understanding the detail of that review and the timing of that review and when I see that I will consider it very carefully.”

She added it is “important” for public service broadcasters to have a “responsibility to the people who work with them”.

The minister was also questioned about the possibility of the Elgin Marbles being returned to Greece, which has long been demanded by the country.

Ms Frazer said: “In terms of sending things back to other countries, the position actually is that the trustees of a museum hold the decision on what to do with the objects under their care.”

She added it can be “not legal for the trustees of the museum to return things” and the Government has no “intention” of changing the law.

Ms Frazer also said: “They can do things around the parameters of whether they return them or not, for example, they may wish to loan them.”

She added: “I don’t have any desire to change the position at all.”

British Museum chairman George Osborne, the former chancellor, has said he is exploring ways for the Parthenon Sculptures, which were removed from Greece by Lord Elgin in the early 19th century, to be displayed in Greece.

The 1963 British Museum Act prevents the institution giving away objects from its collection except in very limited circumstances.

We should ensure that the BBC, as a public service broadcaster... which is meant to be there to provide impartial news to the public, fulfils that duty. Unfortunately, it doesn’t always get that right

Ms Frazer also commented on the future permanent replacement for former BBC chairman Mr Sharp, saying: “I will be appointing the best person to the job and I will not be taking into account of their political persuasions one way or the other.”

She also said: “I am going to set out the process and the charter and there will be a fair and open competition.

“The process in the charter says that the governance code on public appointments applies, I will be following that (and) I will make sure that there is the broadest field possible.”

Dame Elan Closs Stephens will step into the role after Mr Sharp’s resignation last month.

Ms Frazer also said that “on occasion” the BBC is “biased” and the TV licence fee is “one” of the ways to fund the corporation.

When asked for an example of bias, she said she was not going to give “any specific” case.

Ms Frazer also said: “It is really important that the BBC takes its responsibility, in terms of editorial standards and impartiality, very seriously… I think (director-general) Tim Davie takes that responsibility very seriously.

“We should ensure that the BBC, as a public service broadcaster… which is meant to be there to provide impartial news to the public, fulfils that duty. Unfortunately, it doesn’t always get that right.”