Fran Cotton, the former RFU vice-chairman, has agreed to lead an external review into the whole England set-up, which will shine the spotlight on both Johnson and his immediate boss Rob Andrew.
Twickenham's legal officer Karena Vleck will also start to investigate all the allegations of player misconduct, which dogged England throughout the tournament.
Johnson, whose contract expires at the end of December, has been given until Monday week to indicate whether he wants to be considered for reappointment.
Even if Johnson throws his hat back in the ring, the pressure appears to be mounting for significant changes at the top of the England structure.
Cotton has already gone on record this week criticising the lack of progress made by England in the three years since Johnson took charge.
"It has obviously not been a good World Cup by any standards for us," said Thomas.
"We are unhappy with what happened on the field. England should deliver better than it has. The off-field performances have been wholly unacceptable.
"I wouldn't say his (Johnson's) credibility has gone but there are question marks over the coaches and what they've done for him.
"There are clear issues there and similarly there are clear issues over the management of the players.
"We've had, without a doubt in my mind, the worst record off the field. And that's just unacceptable for England.
"Martin has been let down by a number of the players. Martin has accepted the buck stopped with him."
Thomas insisted England would not rush any appointment if Johnson left or was overlooked - and he did not rule out recruiting a caretaker coach for the Six Nations if needs be.
"We have to ensure we don't just rush in and say 'we have to appoint someone come what may before the Six Nations'," said Thomas.
"I really want to make sure we get this right this time. If we have to appoint a temporary coach to see us through the Six Nations, that's fine.
"As far as I'm concerned this time we do it right. We've wasted a lot of time since 2003."
Andrew's position in charge of elite rugby will also come under fresh scrutiny from Cotton, who will report back to the RFU with his recommendations at the end of November.
Andrew announced on Sunday he had accepted the position as the RFU's new professional rugby director, but that claim was shot down by Thomas.
Cotton will assess the best man to head up the elite structure, a process that could open the window for the potential return to the RFU of Sir Clive Woodward.
"I would not make an appointment of a professional rugby director in the light of what has happened here until such time as I've received Fran Cotton's report," said Thomas.
"We have got to, almost as of right, be in the top three within the world rankings.
"I cannot accept that we should ever be out of the top three, with our playing strength, with the skills we've got."
Woodward is unlikely to be available until after the 2012 London Olympics.
England's failed World Cup campaign will now be the subject of three separate reviews - one conducted by Cotton, one on behalf of the Professional Game Board and one from Andrew.
"The Minister for Sport, Hugh Robertson, telephoned me and said he had read reports that there would be internal reviews being conducted," Thomas said.
"He felt it needed more than that and I informed him I had already put that process in place and that I had asked Fran Cotton to chair that group externally to look at the World Cup campaign, to look back at the performance of the England team over the last three years and to look at the functioning of the professional rugby department within Twickenham."
Meanwhile, the RFU have launched an investigation into all allegations of player misconduct during England's World Cup campaign.
Any player found to have breached the RFU's elite player agreement or their code of conduct could face punishments ranging from a fine to an international suspension.
"On Monday I spoke to Karena Vleck, the legal officer, and she will be investigating all the allegations of misconduct off the field," said Thomas.
"She will deal with issues in relation to breach of the elite player squad agreement and indeed, in fact, in terms of the code of conduct we put in.
"The appropriate action will be taken against those players.
"Under the terms of the elite player squad agreement they can be fined in relation to their match fees, they can be fined or cautioned in relation to breaches of the player code of conduct.
"It is open to discussions with Rob Andrew and the England team manager that they would not be available to England going forward as a fairly significant sanction."
England's disciplinary issues ranged from a drunken night out in Queenstown to Manu Tuilagi jumping from a ferry into Auckland harbour, for which he was fined £3000 by the RFU.
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