Campaigners and families of those affected by the contaminated blood scandal are boycotting a meeting with Department of Health officials over the remit of a UK-wide inquiry.
Members of several groups have rejected the Government's proposed process for consultation on its scope, saying the department should not be involved in setting up an inquiry when it is under investigation itself.
The Prime Minister announced last week that an inquiry would be held into the events of the 1970s and 1980s which left around 2,400 people dead.
Thousands of haemophiliacs and other patients were given blood products infected with hepatitis C and HIV.
Mrs May has said their treatment was an "appalling tragedy" which should never have happened.
In a letter to Mrs May, Liz Carroll, chief executive of the Haemophilia Society, turned down an invite to Thursday's meeting at the Department of Health.
She said: "Campaigners, key MPs and the Haemophilia Society have all strongly argued that the DH must not be involved in deciding the remit and powers of an inquiry that will be investigating the actions of its ministers and staff.
"I am sure you can imagine the distress and distrust this would cause for those who are so desperate for the truth to be told.
"I call on you to ensure this inquiry is passed to another department and the meeting cancelled until such time it can be reconvened with adequate notice and to include all those whose voices need to be heard."
A joint statement from groups including Tainted Blood, the Forgotten Few, Positive Women and the Contaminated Blood Campaign said: "We and our members universally reject meeting with the Department of Health as they are an implicated party.
"We do not believe that the DH should be allowed to direct or have any involvement into an investigation into themselves, other than giving evidence. The handling of this inquiry must be immediately transferred elsewhere."
The meeting is still believed to be going ahead.
A Department of Health spokeswoman said: "We are absolutely committed to a thorough and transparent inquiry.
"To establish the best format and remit, we want to hear as many opinions as possible. Our door is open for anyone who wants to discuss the inquiry or raise any concerns."
Downing Street insisted the inquiry would be independent and concerned parties would be asked whether they wanted a judge-led inquiry or a Hillsborough-style panel.
The Prime Minister's official spokesman: "This is going to be an independent inquiry.
"Officials from the Department of Health and the Cabinet Office have offered to meet people affected to discuss the issues and understand their preferences."