The Human Rights Watch (HRW) organisation said its five-year study had found "credible" evidence, corroborated by Pakistani officials, that UK intelligence was aware of the abuse.
Based on interviews with the suspects, their families and lawyers, the report concluded that, while there was no evidence of direct involvement, "UK complicity is clear".
Four of the individuals met British officials while detained in Pakistan, the report said, at times when "clear and visible signs of torture" including the removal of fingernails, were evident.
One Pakistani intelligence source told HRW that British and American agents involved in one case were not just "perfectly aware that we were using all means possible to extract information" but "grateful that we were doing so".
Ministers have denied any policy "to collude in, solicit, or directly participate in abuses of prisoners" or to cover up abuses and have firmly resisted demands for an independent probe.
Two influential Commons committees have backed an inquiry after raising serious questions about the UK's involvement and suggesting the Government could be in breach of international obligations.
There have been a string of allegations about the involvement of UK intelligence agencies in the questioning of terrorist suspects abroad, including supplying questions for interrogators to ask.
Scotland Yard is conducting criminal investigations into claims that MI6 was complicit in the abuse of Binyam Mohamed, a British resident who alleges he was tortured while being held at sites in Pakistan, Morocco and Afghanistan, and the case of a non-Briton.
John Scarlett, the then head of M16, insisted in August that there had been "no torture and no complicity in torture" by the British secret service.
In a series of demands on ministers, HRW called for "a full and independent public inquiry with subpoena powers" to investigate the claims of collusion and the publication, promised by Prime Minister Gordon Brown earlier this year, of the guidance issued to intelligence services.
All allegations of complicity should be investigated, it said, with prosecutions brought where there was sufficient evidence "regardless of position or rank".
And Britain should take "all necessary measures" to ensure torture was not used.
"British intelligence and law enforcement colluded with and turned a blind eye to the use of torture on terrorism suspects in Pakistan.
"British officials knew that Pakistani intelligence agencies routinely used torture, were aware of specific cases and did not intervene," HRW's senior South Asia researcher, Ali Dayan Hasan, said.
Such complicity had been confirmed by unnamed UK and Pakistani officials, the report said.
"A key lesson from the past eight years of global efforts to combat terrorism is that the use of torture and ill-treatment is deeply counter-productive," Mr Hasan went on.
"It undermines the moral legitimacy of governments that rely on it and serves as a recruiting tool for terrorist organisations.
"The evil of terrorism does not justify participating in or using the results of torture. Until an independent inquiry is held and those responsible held accountable, Britain's reputation as a rights-respecting nation will stand tarnished."
A Foreign Office spokesman said: "The Government rejects in the strongest possible terms the suggestion that a policy of complicity in torture has been in place.
"The report's allegations are not new and we have responded to them in Parliament. Some of these cases have already been considered and rejected by the UK courts.
"We have taken a leading role in international efforts to eradicate torture. There is no truth in suggestions that the Security and Intelligence Services operate without control or oversight.
"There is no truth in the more serious suggestion that it is our policy to collude in, solicit, or even directly participate in abuses of prisoners. Nor is it true that alleged wrong-doing is covered up."
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