Ward's conviction was described by peers as one of the "most significant miscarriages of justice in modern British history" as ministers were urged to open up their archives on the case.
The 1963 scandal led to the downfall of then secretary of state for war, John Profumo.
He was introduced to showgirl Christine Keeler by society figure Ward, who was later found guilty of living off immoral earnings and died as a result of an overdose of sleeping tablets.
Labour's Lord Dubs said in the House of Lords: "It seems to me part of a cover-up that has gone on since 1964. The conviction of Stephen Ward is probably one of the most significant miscarriages of justice in modern British history. While the establishment got its scalp, justice was not done." He said it was "very likely" papers relating to the trial would "exonerate Stephen Ward and put right this enormous miscarriage of justice".
For the Ministry of Justice, Lord Ahmad of Wimbledon said the Government could not identify a full transcript of the case in its records. "Full transcripts are not automatically created unless ordered by the judge or requested by the parties involved in the trial," he said. "The National Archives and the Crown Prosecution Service hold partial records of witness evidence given in the trial but a full transcript of proceedings may never have been created.
"The partial records do contain sensitive information about people who are still alive. Exposing such records would invite renewed and potentially unfair speculation about their activities. Accordingly these records will not be released at this time."
He said the case was being reviewed by the Criminal Cases Review Commission.
Liberal Democrat QC Lord Thomas of Gresford said he could not see "any reason" why papers relating to the trial could not be released. "The trial was fully reported in lascivious detail by the Times at the time in July and August 1963 with full page and verbatim accounts of the cross-examination and summing up," he said.