A UN human rights advocate has called on Britain and the US to release confidential reports into the countries' involvement in the kidnapping and torture of terrorism suspects, accusing them of "years of official denials, sophistry and prevarication" to cover up the truth.

In a speech to the UN human rights council in Geneva introducing a report on the issue, Ben Emmerson, a British barrister who is the UN's special rapporteur on protecting human rights within efforts to combat terrorism, demanded that Britain publish the interim findings of a report by a retired judge, Sir Peter Gibson, into the involvement of MI5 and MI6 in the removal and mistreatment of terrorist suspects.

In a response delivered at the council, British officials said the government was "looking carefully at the contents of the report by the Gibson inquiry on its preparatory work, with a view to publishing as much of it as possible". There was no word on when this might happen.

Emmerson also asked the US to release a similar report by the Senate's select committee on intelligence into the CIA's secret detention and interrogation programme.

Failure to do so showed a seeming unwillingness by both governments to face up to serious international crimes and "a policy of de facto immunity for public officials who engaged in acts of torture, rendition and secret detention, and their superiors and political masters who authorised these acts", Emmerson said.

"Words are not enough. Platitudinous repetition of statements affirming opposition to torture ring hollow to many in those parts of the Middle East and North Africa that have undergone, or are undergoing, major upheaval, since they have first-hand experience of living under repressive regimes that used torture in private whilst making similar statements in public," he added.

"The scepticism of these communities can only be reinforced if western governments continue to demonstrate resolute indifference to the crimes committed by their predecessor administrations."

Britain and the US have come under increasing pressure as details emerge of the so-called secret rendition programme, in which terrorism suspects – some wrongly identified – were often snatched off the streets and flown to either secret CIA prisons or detention centres operated by other countries, for example Egypt, where many complained of torture and other mistreatment.

On Monday, a Libyan politician suing the former foreign secretary, Jack Straw, and the British government for damages after being kidnapped at Bangkok airport and sent to jail in Tripoli, where he was tortured and also interrogated by UK intelligence officers, offered to settle the case for £3, so long as he receives an unreserved apology.

Despite government efforts to keep such acts secret, Emmerson said, more and more details had emerged, "and calls for accountability are fast approaching a critical mass".

He makes a series of specific recommendations in the associated report, including a call for 35 countries that had failed to respond to questions from a UN study on secret detention to do so, and that Britain and the US should release their reports.

Shortly before the speech, Emmerson told the Guardian it was time for "a reckoning with the past".

He said: "In South America it took up to 30 years before the officials responsible for crimes like these were held fully accountable. With the conspiracy organised by the Bush-era CIA it has taken a decade, but the campaign for securing the right to truth has now reached a critical point.

"The British and American governments are sitting on reports that reveal the extent of the involvement of former governments in these crimes. If William Hague is serious about pursuing a policy of ethical counter-terrorism, as he says he is, then the first thing the British government needs to do is to release the interim report of the Gibson Inquiry immediately."

The Gibson report was announced by David Cameron in July 2010. However, rights groups and victims' lawyers decided not to take part when it emerged the inquiry would have no power to compel official cooperation or evidence. In January 2012, the government said the inquiry was being scrapped owing to police investigations into alleged crimes. However, Emmerson said, there were no prosecutions pending and the government should publish an interim version of the report handed to them by Gibson in July last year.

Emmerson's report into the issue goes into greater details about what has so far been uncovered about the US network of secret detention facilities for terrorism suspects and other countries' complicity in the process.

It says: "There is now credible evidence to show that CIA 'black sites' were located on the territory of Lithuania, Morocco, Poland, Romania and Thailand and that the officials of at least 49 other states allowed their airspace or airports to be used for rendition flights."

Despite the scale of this, the report notes, just one criminal case has been brought, when an Italian court in 2009 convicted 22 CIA agents in absentia along with Italian intelligence service officials over the case of an Egyptian-Italian national kidnapped in Milan and sent to Cairo, where he was tortured.