The five include Rangzieb Ahmed from Manchester, who was later convicted by a British court on terrorism charges and was said to have been al Qaeda's top operative in Britain.
He has alleged his fingernails were pulled out by Pakistani agents before being questioned by British officials soon afterwards.
Another suspect was Rashid Rauf from Birmingham who was wanted by Britain for his alleged part in a major bomb plot.
"The government rejects in the strongest possible terms the suggestion that a policy of complicity in torture has been in place"
UK government statement
He was apparently so badly beaten that a British intelligence official told HRW researchers he could never appear in court.
HRW said British authorities had put Pakistan under pressure to extract information from the suspects and was unconcerned about how the detainees were treated.
The group quoted two unnamed British government sources, as well as Pakistani military officials, to support its claims over the alleged mistreatment.
"British officials knew that Pakistani intelligence agencies routinely used torture, were aware of specific cases and did not intervene," the group's report said, listing allegations of prisoners being beaten, chained and injected with drugs.
Hasan told Al Jazeera that British agents colluded in multiple ways.
"They passed questions and lines of inquiry onto suspects while the suspects were in ISI [Pakistan's intelligence service] custody, and in the custody of other Pakistani intelligence agencies," he said.
"The ISI's reputation as an institution that tortures terrorism suspects is well established. The idea that they could not have known of these practices is laughable."
In response to the report, Britain's foreign office said there was "no truth" in claims that it was "our policy to collude in, solicit, or even directly participate in abuses of prisoners.
"The government rejects in the strongest possible terms the suggestion that a policy of complicity in torture has been in place," a spokesman said.
Hasan criticised the government's response saying that the rights group, as well as the media, offered the British government specific allegations and cases and what they got in return was "a generic denial".
"We want to know what happened in [individual] cases," Hasan said.
"The government is stonewalling, we would like closure on this activity."
The report adds to growing calls in Britain for an investigation into such claims.
In August, a UK parliamentary committee on human rights called for an independent inquiry into claims of British complicity in torture.
Meanwhile, police are looking into claims from Binyam Mohamed, a former Guantanamo detainee who says that the security service, MI5, was complicit in the "medieval" torture he suffered in Pakistan, Morocco and Afghanistan.
Britain's foreign intelligence organisation, MI6, is also being investigated in a separate abuse case.