Baroness Butler-Sloss, the retired judge heading the UK government's inquiry into child sex abuse, came under increasing pressure today after a report emerged that she kept allegations about a Church of England bishop out of an important review into paedophile priests in one diocese.

The Times on its front page reports today that Lady Butler-Sloss told a victim of alleged abuse that she did not want the claims about the bishop to be in the public domain because she "cared about the Church" and "the press would love a bishop."

The report is by one of the country's top crime journalists, Sean O'Neill, who has consistently led the field with accurate reports of his investigations into child abuse.

According to The Times, the revelations have prompted fresh calls for the peer to step down as chair of the new inquiry.

The newspaper reports that her comments were made in 2011, during a meeting at the House of Lords with Phil Johnson, a survivor of assaults by clergymen when he was a choirboy in the Chichester diocese. Mr Johnson, who is now a member of a national safeguarding panel for the Church of England, kept a detailed record of the meeting. The Times reports that he felt "pressured" into agreeing to withhold the allegations from the review.

The bishop was charged this year with indecent assault offences and misconduct in a public office.

Earlier this week The Guardian reported that Lady Butler-Sloss's child abuse role is in doubt because of a row over a conflict of interest. Lady Butler-Sloss was criticised over fact her brother Lord Havers was attorney-general at time of some of controversy. Some lawyers and leading MPs, including the new chair of the health select committee, urged her to stand aside.

The Home Office said earlier this week that she would not be asked to step aside.

Lady Butler-Sloss, aged 80, told the BBC that she had been unaware of reports that her brother tried to prevent ex-MP Geoffrey Dickens airing claims about a diplomat in parliament in the 1980s. She said: "I know absolutely nothing about it. If people think I am not suitable, then that's up to them."

Alison Millar, a lawyer who has represented many victims of child abuse, told the BBC: "Survivors of abuse have a deep and well-founded distrust of authority figures given the breach of trust they have experienced as children. To enable them to be able to believe in the findings of this inquiry and for it to be seen, in their eyes, as a safe environment in which to talk about their experiences, there can be no shadows of doubt cast by links to allegations of an establishment cover-up.

"Whilst Baroness Butler-Sloss is a person of enormous integrity, the concern is that she is just too close to the establishment and in particular, concern over her family connection to Sir Michael Havers."

Labour MP Simon Danczuk, who has played a leading role in calling for an investigation into child abuse allegations, told The Times that the peer's position now seems "untenable".