England have lost 13 of their 22 Tests under Robinson, who is due to meet his Rugby Football Union bosses now the autumn international series has ended.
Former England hooker Brian Moore has joined the clamour for Robinson to go.
In Monday's Daily Telegraph he writes: "I strongly suspect that the decision that Robinson must go was really made after the Argentina game and, if so, it should have been executed at that time because all else was disingenuous.
"It will be interesting to see who announces the decision and who takes responsibility for it. Rob Andrew must be that person as he must be seen to be in control of this area and to accept responsibility for his choices.
"He must also lead the search for a replacement."
Andrew is the RFU's elite director of rugby.
Moore wants England World Cup-winning captain Martin Johnson to take over.
He said: "I see no reason why Martin Johnson could not successfully fulfil the manager's role. Enormous credibility and recent knowledge of the players available for England would be allied to a deceptively sharp brain and every effort should be made to get him to at least consider the offer."
Phil Vickery has urged Twickenham's hirers and firers not to do "anything silly" as Robinson seemingly lurches towards the end of his reign.
World Cup winner Vickery's plea looks certain to fall on deaf ears though, with an outside chance the 42-year-old head coach could even depart later on Monday.
Robinson says he will fight tooth and nail, yet an unacceptable autumn Test series scarred by a record home defeat against New Zealand, a first Twickenham loss to Argentina and then South Africa ending their nine-year wait for a win at English rugby headquarters has taken its toll.
He is due to head off for three days of World Cup planning business in Paris on Tuesday, but his employers should save him the bother because there is little chance he will be around for England's tournament opener against the United States on September 8 next year.
A 25-14 home defeat against South Africa, after England led 14-3 approaching half-time, undoubtedly proved the final straw - despite Vickery and several other players backing their boss.
The Wasps prop said: "It is not rocket science to work out after a performance like that, we are not favourites to win the World Cup.
"But we have got good players, and we hope to get others back from injury."