Britain is a "partner in crime" with the United States in organising secret flights to move terror suspects around the world, a human rights groups says.
Amnesty focused on the cases of two Guantanamo detainees
Amnesty International claims that UK ministers have adopted a "see no evil, hear no evil" approach to CIA flights.
It has called on Britain and all other EU states to stop their airports from being used for the practice.
The UK government previously said it had approved two US prisoner flights and refused two others since 1998.
On Wednesday, a Foreign Office spokesman said: "This report adds nothing new to the debate. We have said everything we want to say on this issue."
Amnesty has called for a public inquiry into the flights - known as "extraordinary renditions" - because it says domestic and international laws have been broken.
Its report comes the week after human rights watchdog the Council of Europe named Britain as one of 14 European countries which colluded with the CIA.
The Amnesty report tries to put Britain's fingerprints on the cases of two men - Bisher Al-Rawi, 38, and Jamil El-Banna, 44.
They were arrested after flying to Gambia in November 2002 and eventually ended up in Guantanamo Bay - where they are still being held.
Amnesty claimed their travel arrangements were passed to the US and as a result the government was "instrumental" in their detention.
Bosnia and Herzegovina, Germany, Italy, Macedonia, Sweden and Turkey have also been involved in the flights, the report claims.
The report's authors focused on a further five cases of rendition involving six European states and 11 victims.
The report said all of the cases involved "men being bundled on to planes and transferred abroad, where they have suffered abuse".
It said: "The impact on both them and their families has been devastating.
"This report highlights the role of various European states and shows how the action or lack of action by these states contravened their obligations under domestic and international law."
Last week at prime minister's questions Tony Blair told MPs the Council of Europe report contained "absolutely nothing new".
Liberal Democrat leader Sir Menzies Campbell asked him to confirm that the UK had given no logistical support to the CIA on the flights - known as renditions - nor given information to be used in torture.
The prime minister said the government had said all it had to say on the issue and repeated the government's insistence that since 1998 it had agreed to two US requests for prisoner flights through the UK, and refused two others.