Mr Cummings sparked fury among Tory MPs and the wider public after it emerged on May 22 that he had driven from his London home to his parents’ farm estate in County Durham, with his wife suffering from suspected coronavirus symptoms, at the height of the lockdown in late March.
Nazir Afzal, former north west chief crown prosecutor, said Durham Police, the Met and the CPS had "closed ranks" on the issue and questioned why more action was not being taken, The Guardian reports.
He and his lawyers have now started preparing evidence on Cummings’ lockdown movements at the height of lockdown and have also issued an appeal to the public for help.
Mr Afzal said: "Contrary to my experience while in post, neither the police nor the CPS appear to have an interest in this important issue of deep public concern."
He added: "It doesn’t fill me with much confidence that they chose to close ranks when the recent survey shows that public compliance with the lockdown regulations was significantly impacted by the actions of Cummings and the inadequacy of the government and police response.
"You have to ask, what do they have to hide and whose side are they on?"
Last month, Mr Afzal's lawyers urged the CPS and the Met to thoroughly investigate Mr Cummings' lockdown trip and asked Durham Police to reopen its investigation into the chief aide's movements.
The lawyers said they were "concerned that the short investigation, undertaken in a highly charged political environment, and in a rushed manner, did not ascertain or consider the totality of the evidence available".
Mr Afzal's requests have been rejected by both police forces and the CPS, his lawyers said.
"It would not be prudent for resources to be spent on the same or similar allegations," the Met said in a letter to Mr Afzal.
Durham Police did not add to its press statement released in May which found Mr Cummings had most likely breached health protection regulations during his trip to Barnard Castle.
The CPS said it would not take action unless invited to do so by the police.
Mr Afzal's solicitor, Mike Schwarz, from Hodge Jones and Allen, has now urged witnesses to come forward who can "shed light on Mr Cummings' activities" in March and April.
"We are driven by what others should be doing - compiling a dossier of evidence and making our own assessment as to whether a prosecution should follow and presenting it to the director of public prosecutions," he said.
It comes after new research suggests Mr Cummings' trip to Durham damaged the public's trust in the Government's handling of the coronavirus pandemic.
In a series of interviews, diaries and surveys, researchers at think tank British Future found that people "became notably angrier when describing politicians" after the controversy emerged.
"Public trust in the Government’s handling of the Covid-19 crisis fell after the Prime Minister’s adviser Dominic Cummings was seen to break lockdown rules," the report says.
"Participants became notably angrier when describing politicians in the later discussion groups and in their diary entries."
Researchers also found that most people disapproved of Mr Cummings' actions regardless of their political views.
"The perception that the Prime Minister’s adviser Dominic Cummings had broken lockdown rules was a highly salient issue that appeared to damage trust in politicians," the report notes.
"It was not, however, as divisive an incident as might be thought. Most people, irrespective of their political views, appeared to disapprove of Cummings’ action."