A total of 23 individuals, some of whom suffered alleged abuse in childhood, sent Mrs May a letter claiming the inquiry is "not fit for purpose".
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Is she trying to limit the inquiry to spare the reputation of paedophile politicians?
Peter Saunders, chief executive of the National Association for People Abused in Childhood (Napac), said his organisation would withdraw its co-operation if Mrs May does not pledge to give additional powers to the beleaguered inquiry, by granting it statutory status.
"We are the largest survivors' group and we have some very significant concerns about this inquiry," Mr Saunders said. "Mrs May has said she is willing to meet us about our requests but if she says no we will probably walk away. I am not hopeful that we will get what we want."
"The Home Secretary has said she is willing to consider granting the inquiry statutory status at some point in the future but that she will not do so at this stage. "We think this is wrong - it's a deal-breaker."
The letter to Mrs May said the 23 signatories were declining an offer to attend the meeting on Friday.
"We, alongside many survivors, have made numerous representations to you regarding our view that the Inquiry as it stands is not fit for purpose," it said.
"The Home Office seems to be running the inquiry to meet others’ needs rather than those of survivors and the public. "We therefore have little option but to end engagement with the Inquiry and call on other survivors, whistleblowers, associated professionals and agencies to follow suit."
The letter said the inquiry's terms of reference went "well beyond the original declared intentions ... to investigate government and establishment cover-ups of paedophiles in their ranks".
It accused Mrs May of failing to address potential conflicts of interest among members of the panel inquiry, after two people appointed to chair it had to resign for similar reasons.
The period to be examined should be extended from 1970 to 1945, the letter added.
The letter suggested the signatories would resume co-operation if the current panel was scrapped and replaced "on a transparent basis".
They also said Mrs May must grant it statutory powers, which would allow officials to seize more evidence and demand the attendance of witnesses.
Fiona Woolf, the head of the child sex abuse inquiry, resigned in October after questions were raised about her links with Lord (Leon) Brittan, whose role as home secretary in the Eighties is expected to come under scrutiny.
The City lawyer, who is also Lord Mayor of London, was the second chairman to have to step down after the Home Office failed in both cases to properly investigate potential conflict of interest in their background.
Baroness Butler-Sloss, a retired judge, resigned in July after it emerged her late brother had been attorney general during part of the period under examination and may have been involved in taking legal decisions connected with sex abuse allegations.
Mrs May told Sky News that she was aware of the letter. "The issues in the letter have been spoken about before," she said. "But I am clear we have a once-in-a-lifetime opportunity to get to the bottom of this issue."
A Home Office spokeswoman said: "The Home Secretary is absolutely committed to ensuring the Independent Panel Inquiry into Child Sexual Abuse has the confidence of survivors and that is why she is meeting them and their representatives to hear their views and to ensure the right person is appointed to lead the inquiry panel in its vital work."