Martyn Thomas quit as chairman on Sunday after the findings of a review into John Steele's nine-month stint as chief executive were reported to the RFU council.
High Court judge Jeff Blackett, the RFU's chief disciplinary officer, chaired the five-man panel, which was charged with looking into how the RFU was governed during the reign of Steele, who left his post last month.
Blackett's findings came down strongly on Thomas, and his 52-page report called on the chairman and eight of nine non-executive board members to stand down immediately.
Thomas, who remains as acting chief executive, warned he could take legal action if the report was published.
Although that threat is now believed to have been lifted, the RFU could yet lose another senior figure with Blackett understood to be considering his position.
Steele's predecessor Baron now fears the saga could cause jitters in the international rugby community, and he told BBC Radio Five Live: "(The World Cup in) 2015 is so important for rugby in England.
"It's a great honour to host the World Cup and I'm delighted that, on my watch, we were able to secure that right.
"What is worrying me now is what the IRB (International Rugby Board) is thinking about and the other major unions in the world are thinking about when it appears the RFU can't even manage its own business.
"My worry is that they're starting to say, 'Can we risk the RFU managing the World Cup in 2015?' And that would be absolutely horrendous for the game.
"That's why it is so important that we move quickly and decisively. The Blackett report has to be published, the recommendations have to be implemented."
The IRB is understood to be reluctant to get involved in what it sees as an internal affair but Baron has been horrified by the events of the past week.
He added: "What I am really concerned about is that, through the threats of legal action, the chairman and the board (of the RFU) seem to have been able to get a report that they commissioned suppressed because they didn't like its conclusions. That is unprecedented."
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