Having been cleared of a potential misconduct charge, acting chief executive Thomas called for the departures of Blackett and two council members, after announcing his own decision to stand down from the RFU with immediate effect, over a fortnight earlier than originally planned.
Thomas had been criticised in the Blackett Report - compiled with the assistance of council members Geraint Ashton Jones and Malcolm Wharton - into the hiring and firing of John Steele as chief executive.
Blackett had indicated on September 2, during an RFU council debate on a vote of no confidence in Thomas, that he had sufficient evidence to bring disciplinary charges.
Charles Flint QC was subsequently engaged by RFU president Willie Wildash to determine whether any action should be taken against Thomas.
Flint's report, published on Tuesday, concluded that there was "no solid evidence which could support a charge" of conduct prejudicial to the interests of the game.
Thomas said: "I am obviously pleased by the news today though I have always believed and said that process of the Blackett Report was flawed.
"I take no pleasure in being proven right as it has turned the Rugby Football Union on its head and caused enormous damage as well as bitter infighting which is deeply regrettable.
"Jeff Blackett and the other RFU council members (Ashton and Wharton) involved in producing the report have caused all this trouble and should do the decent thing and resign immediately."
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