Stephen Deans, the union's official at the centre of the Grangemouth dispute that brought the petrochemical plant to the brink of closure last month, is to stand down as chairman of the local party.
Mr Miliband has refused to reveal details of what the party's investigators found following accusations that Unite attempted to fix the selection of Labour's Falkirk candidate for the next election. However, the Labour leader is under increasing pressure to make the findings public after leaked emails seemed to show the original inquiry had found forgery, coercion, trickery and manipulation.
Senior Tory MP Priti Patel has now demanded Mr Miliband reopen the inquiry. Party members in Falkirk have also called on him to publish the results of the original inquiry, carried out earlier this year.
However, Scottish Labour last night called for the party to move on from the accusations, which have dogged it for months. A spokesman for the party said it was now "focused on ensuring we have a fair and transparent selection and that the local party has a new candidate they can get behind".
But local party sources in Falkirk expressed their dissatisfaction with this stance. One said: "It is just not satisfactory to try to ignore this as if it never happened. But that is exactly what they are trying to do."
As chairman, Mr Deans signed up dozens of new members to the local Labour Party only to find himself at the centre of allegations that Unite was trying to pack the party to ensure its favoured candidate, Karie Murphy, was selected.
Prime Minister David Cameron has also accused Mr Deans of being a rogue operator who single-handedly nearly lost 800 jobs when the Grangemouth petrochemical plant almost closed down for good.
Mr Deans has resigned from his job at Grangemouth after a separate investigation by plant owners Ineos into allegations he was carrying out Labour business while at work. The allegations include claims he attempted to secure the Falkirk selection.
In addition to the claims regarding the findings of the original Labour inquiry, leaked emails released yesterday suggest many of those signed up to Labour during the chairmanship of Mr Deans were "paper members".
In a separate move, Gregor Poynton, would-be candidate for the Falkirk selection, was also reported to have accused former Labour election chief Tom Watson of being "involved in it all behind the scenes".
There had been speculation Mr Deans might be ousted at a meeting of the local Labour Party yesterday at Camelon Labour Club, but his position was not discussed.
Later, a senior Labour source said his post would be facing re-election at the local party's annual meeting in three weeks' time, and that he would not stand for re-election. The source added: "It is understood Mr Deans will not be putting himself forward."
Local members said they were also given that message with a "nod and a wink" during yesterday's meeting, attended by about 30 people.
While the decision by Mr Deans to stand down is understood to have relieved tensions at the meeting, it was still deemed unsatisfactory by some who were present.
A local party source said: "For all intents and purposes Stephen Deans is still in charge of the Labour Party in Falkirk. And that cannot be good for the Labour Party, in Falkirk or anywhere."
Another source described yesterday's meeting as "heated but a total waste of time". Scottish Labour leader Johann Lamont did not attend, despite calls from some local members for her to address them.
Aides said Ms Lamont did not think such a move was appropriate while the local party was still in "special measures", a state of affairs imposed after the vote-rigging allegations surfaced.
However, in an interview during the weekend, Ms Lamont attacked the "arrogance" of those who attempted to stitch up the selection process and pledged an "open, free and fair contest".
Members of the local party executive were addressed by Eric Wilson, the UK party officer who led the fixing inquiry, but he did not talk to rank-and-file members.
Vice-chairman of the Falkirk constituency party, Gray Allan, said: "I want him [Ed Miliband] to publish the report, the constituency wants him to publish the report - everybody I've spoken to wants him to publish the report. He needs to consider how the centre can help to rebuild this organisation so that we are fit and ready to fight the next election and win the seat for Labour.
"Of all the parties that have been involved in this matter since the beginning, the one voice that has not been heard is that of the rank-and-file Party members in this constituency.
"We have heard umpteen reports, allegations and suppositions as to what happened or did not happen."
Labour said it had acted "swiftly and thoroughly" throughout the matter and "will continue to do so".
Unite denies any wrongdoing.
Labour will select a candidate to fight the Falkirk West seat from an all-woman shortlist on December 8.