MP Keith Vaz, who raised questions over Baroness Butler-Sloss' appointment to the abuse inquiry last week, has said the process has become "shambolic".
The Chair of the Home Affairs Select Committee said he was "not surprised" by Lady Butler-Sloss' decision to stand down, adding that "it is the right one".
"As I pointed out to [Home Office permanent secretary Mark] Sedwill, the public would be concerned that a member of Parliament, no matter how distinguished, had been appointed to head this important panel.
"The whole inquiry process is becoming shambolic: missing files, ministers refusing to read reports and now the chair resigning before the inquiry has even commenced."
The Baroness says she did not consider the "difficulties" caused by her background and family connections to the child sex abuse inquiry.
Questions have been raised of former High Court judge Baroness Butler-Sloss since her appointment last week.
22 police officers are now assigned to Operation Fernbridge - the probe into claims of a Westminster cover-up of sex child abuse.