It is understood the PCA asked the commissioner not to display the belt because of fears it could prejudice the inquiry and any prosecution of the three officers suspended over the case.
A march to protest at the death of Mrs Gardner, 40, is to be held today in north London, where she lived.
Senior Metropolitan Police sources said William McCall, the PCA's lay official supervising the inquiry by Essex Police into Mrs Gardner's death, had also been unhappy about Mr Condon holding a press conference to announce the suspensions of the officers and the deportation squad.
Mr Condon, who went ahead with the press conference on Tuesday, wanted to display the belt, which is believed to have hand and possibly leg cuffs attached by chains, in order to end speculation on its precise nature. Critics of the police have claimed the belt has fittings for ankles and neck.
The authority said its investigations under the Police and Criminal Evidence Act were more tightly controlled than in a conventional criminal inquiry. 'It is not a question of whether we want to display a piece of evidence or not, we are simply unable to under the law.'
Meanwhile Bernie Grant, Labour MP for Tottenham, said he would make a formal protest to the Press Complaints Commission over an article in the London Evening Standard, which he accused of trying to stir up a race riot. Mr Grant, who has led calls for an independent inquiry into Mrs Gardner's death, said he had been shocked by the newspaper's coverage. Senior Scotland Yard officers are also said to have been concerned.
The front page of Thursday's edition said the 'fragile peace' forged following Mrs Gardner's death looked certain to be 'blown apart' after claims that she was gagged with tape. The paper expressed fears that today's demonstration would become a 'march of hate'.
'They were printing factually incorrect material with a view to stirring up a race riot,' Mr Grant said. There had been no indication that there would be trouble. 'Hornsey is a white, middle- class area. The local people are not going to riot. Much of the anger has been dissipated by the prompt action of the Commissioner of the Metropolitan Police,' he added.
The PCC said concern had been expressed over the Evening Standard article, but a formal complaint had yet to be received. Craig Orr, the paper's managing editor, said he could not comment until notification of an official complaint.
Today's march, past Hornsey police station, is expected to be heavily policed.
The Police Complaints Authority is to investigate the death of Mohammed Nazir, 57, a taxi driver who collapsed while police inspected his cab yesterday at a council depot in Slough, Berkshire, after midnight. A post-mortem examination was reported to have found the cause of death to be heart disease.