In a statement sent to Planning this week, the Blakelands Residents Association claimed it had asked the police to investigate issues in relation to a warehouse development granted permission by the council in January 2018.
This consent allowed for the construction of a replacement of the existing 10.5-metre high warehouse with a new 18.4 metre high structure.
However, according to the campaigners, the permission "omitted 13 key conditions, most of which were designed to protect the amenity of the neighbouring residents".
According to minutes of a Milton Keynes Council development control committee meeting in January last year, the committee had "apologised on behalf of the council for the error".
It added that members of the committee had "sought clarification as to what other measures could be undertaken to address the situation and seek to mitigate the impact of the error on residents in the immediate vicinity of the development".
The council subsequently announced that it had commissioned an independent review of the permission for the warehouse. The review, being undertaken by independent planning consultant Marc Dorfman, was due to be published in October last year but has been delayed.
The statement from the residents groups claimed that the body has conducted its own investigation into the circumstances surrounding the grant of planning permission.
The group said that, earlier this month, it "made an allegation to Thames Valley Police of misconduct in public office", supported by "a 207 page case file documenting the full factual history and all the evidence".
Thames Valley Police has confirmed that they have been asked by the group to investigate the matter.
Blakelands Residents Association has also called on the secretary of state "to intervene and exercise his powers to order an independent inspection".
"We consider that such an inspection is both necessary and proportionate given the long-history of serious failings and poor service delivery", the statement said.
A letter seen by Planning from the council's chief executive Michael Bracey to the residents' association states: "We acknowledge improvement is required in our planning service. That is why we have set up a Planning Improvement Board... The work of the board is now well underway, and progress is being made."
Elsewhere, it states: "Finally, whilst I am very concerned about the allegations you make about misconduct in public office, it is not for me to comment on a matter that has been formally passed to the police. They will decide if there is a case to investigate or not."
In response to the claims made, a spokesman for Milton Keynes Council said: "An independent review of this planning decision is underway and the council will consider and respond to the recommendations made following the completion of the review."