Drusilla Sharpling, one of four panel members, told MPs yesterday: "At the end of April, with the panel's knowledge, I reported my concerns about the leadership of the inquiry to the then director general of the Home Office, Mary Calam.
"I was alerting them. I felt they had the right to be informed."
Ms Sharpling said she and her fellow panel members, including the current chairman Professor Alexis Jay, had become increasingly concerned about Dame Lowell's leadership.
But she insisted that while voicing her worries with the senior civil servant she had not given "anyone permission to spread these concerns amongst anybody else" and did not "require any action to be taken".
The Home Affairs Select Committee was also told of the breakdown in relations between Dame Lowell and the other members of the IICSA panel in the months before her resignation.
At one stage a 'facilitator' was brought in to try to improve relations during meetings but to no avail.
Prof Jay told MPs: "It was clear from the beginning that Lowell Goddard really would have preferred to sit on her own without the assistance of a panel.
"As a consequence of this view that was conveyed to us, we did feel that we were kept at a distance from a lot of the activities of the inquiry."
Ivor Frank, a third panel member, said: "There were times when things were perfectly amicable and perfectly professional. There were other times when it was less the case."
One MP said last night it seemed extraordinary that Mrs May and other Home Office ministers at the time could not have been aware of the mounting tensions.
"This evidence session reveals an astonishing level of dysfunction in the child sex abuse inquiry over the last year. How could ministers not have known?" said Labour MP Lisa Nandy.
The Home Office is accused of misleading MPs after Amber Rudd, the current Home Secretary, told the committee last month that the judge, who is from New Zealand, had resigned in August because she felt lonely and was "a long way from home", adding: "That's all the information I have."
In fact the Home Office had been made aware of concerns about Dame Lowell's "professionalism and competence" on July 29.
Mark Sedwill, the Home Office permanent secretary, told MPs that the then director general had been made aware of concerns about Dame Lowell in April but said those fears had not been passed either to him, Mrs May or to anybody else in the department.