The Home Office has again been forced to defend the appointment of Lady Butler-Sloss to run the inquiry into allegations of historical child abuse amid claims she refused to go public about a bishop implicated in a scandal.

The retired high court judge is reported to have told a victim of alleged abuse that she did not want to include some of his allegations in a review of how the Church of England dealt with two paedophile priests because she "cared about the Church" and "the press would love a bishop".

The peer allegedly made the remarks to Phil Johnson, who was abused by priests when he was a choirboy, during a private meeting in the House of Lords in 2011, according to the Times.

The Home Office has again insisted it stands by the crossbench peer's appointment "unreservedly". Earlier this week it was forced to defend the appointment when critics pointed out that her late brother, Sir Michael Havers, was attorney general from 1979 to 1987 when some of the controversy over the failure to prosecute child abuse cases could have arisen.

Butler-Sloss insisted in a statement that she had never put the reputation of an institution ahead of justice for victims.

"Throughout many years of public service I have always striven to be fair and compassionate, mindful of the very real suffering of those who have been victims of crime or other injustice. I have never put the reputation of any institution, including the Church of England, above the pursuit of justice for victims," the statement said.

"That is why I am honoured to be leading this inquiry into whether public bodies and other non-state institutions have done enough to protect children from sexual abuse. I am assembling an independent panel of experts so that we can begin this important work as soon as possible."

A spokesman from the Home Office said: "Baroness Butler-Sloss has had a long and distinguished career at the highest levels of this country's legal system. Her work leading the Cleveland child abuse inquiry and as president of the high court's family division make her the perfect person to lead this important piece of work.

"As the permanent secretary (Mark Sedwill) told the home affairs select committee this week, the integrity of Baroness Butler-Sloss is beyond reproach and we stand by her appointment unreservedly."

The Times reports that her comments came during a meeting with Johnson when she was in charge of an investigation into how the church handled allegations of abuse. He made allegations against Peter Ball, the former bishop of Lewes and bishop of Gloucester, who was subsequently charged with two counts of indecent assault and one of misconduct in a public office. A trial is expected to take place in November.

She said she would "prefer not to refer to him", according to the report, but would bring up the allegations in private correspondence to the archbishop of Canterbury. Johnson accepts she passed on his allegation.