Raju Bhatt, one of the solicitors who brought the two High Court judicial reviews in which Dame Barbara conceded defeat last week, said the Attorney General should appoint a judge to conduct the inquiry and report its findings to him.
Amid mounting criticism, Dame Barbara has resisted calls for her resignation, and instead announced an urgent inquiry, after throwing in her hand in the court challenges over decisions not to prosecute officers over the deaths of Shiji Lapite and Richard O'Brien.
Friday's Crown Prosecution Service announcement said the independent outsider who would conduct the inquiry was to report to the DPP herself. But questions were being asked yesterday over potential conflicts of interest.
The terms of reference of the inquiry will be announced today; it is likely the person who will head the inquiry will also be named.
It was not disputed in last week's challenge to the Lapite decision that the case had been sent to the Director for her approval.
According to documents disclosed at a late stage in the O'Brien challenge, this case had also apparently been sent to the DPP for a decision, although a letter produced to the court at an earlier stage in the proceedings said it had not.
Mr Bhatt said: "There is concern that the inquiry is going to be headed by someone appointed by the Director herself and that he or she will report to her. But the director's own role is going to be under scrutiny.
"She is going to have to explain how she came to make decisions that she now accepts were perverse.
"It is anomalous that the inquiry which should be focusing, amongst other things, upon her own role, should be reporting to her."
Mr Bhatt and other lawyers said yesterday that the person heading the inquiry should be appointed by the Attorney General, John Morris, under whose superintendence the CPS operates and who is, in turn, accountable to Parliament, and that the findings should be likewise reported to him.
A CPS spokeswoman responded: "The inquiry will look at decision-making in CPS Central Casework, not at the DPP herself. The results of the inquiry will be made public and a report will be sent to the Attorney General."
Mr Bhatt said that the inquiry should be headed by a judge and urged that thereafter, the Commons Home Affairs Select Committee should scrutinise the entire police complaints process.
"Ultimately, a decision by the Crown Prosecution Service is the culmination of the police complaints process," he said. "The home affairs committee should look at the whole complaints procedure from start to finish."
Alan Whitehouse, the Chief Constable of Sussex Police, told BBC Radio 4's The World This Weekend: "I can say on behalf of my colleagues round the country that none of us wish to retain in the service officers who are unable to control themselves and who use unnecessary force."Reuse content