"The UK has allowed these aircraft to land, re-fuel and take off from their territory," the human rights group's regional director Claudio Cordone said in a statement on Thursday.
"The UK government must launch an immediate, thorough and independent investigation into mounting evidence that its territory has been used to assist in unlawfully transporting detainees to countries where they may face "disappearance", torture or other ill-treatment," he added.
The British government said on Monday it had no evidence that the current US administration had been transporting terrorism suspects through British airports.
Cordone said: "Whether the US is sending people to other countries to be tortured, or snatching them in other countries to be abused in Guantanamo, international law prohibits the UK, or any other state, from aiding or abetting them."
Human rights groups accuse the CIA of running secret prisons in eastern Europe and covertly transporting detainees -a practice known as "extraordinary rendition". They say incommunicado detention often leads to torture.
The Amnesty statement named several men it said had been abducted by the CIA and flown to Jordan and Egypt as part of the US campaign of "extraordinary rendition".
"The UK government must launch an immediate investigation into mounting evidence that its territory has been used to assist in unlawfully transporting detainees"
Amnesty International statement
In each case a Gulfstream V, registration N379P, had stopped to refuel at Prestwick airport in Scotland on its way back to the United States after dropping off its passengers, it said.
It cited the case of Jamil Qasim Saeed Mohammed who it said was seen being bundled aboard the CIA plane by masked men in Karachi on 23 October, 2001. The plane then flew to Jordan and the following day, now without its passenger, it flew to Prestwick and then on to Dulles International airport near Washington.
Amnesty demanded that the United States reveal Mohammed's whereabouts.
Amnesty said that on 12 January, 2002, Indonesian security officials saw Muhammad Saad Iqbal Madni being put on the plane in Jakarta and flown to Cairo. Once again the plane stopped in Prestwick to refuel after depositing its passenger.
It said Iqbal Madni had since been returned to US jurisdiction and was now a detainee in Guantanamo Bay where fellow detainees had said he was on the verge of a breakdown.
Amnesty cited a third case where a Swedish investigation has already revealed that US security officials took Ahmed Agiza and Mohammed al-Zari from Sweden to Cairo for torture.
In total, Gulfstream N379P had been logged between 2001 and 2005 making at least 78 stopovers at British airports while en route to or from destinations such as Baku, Dubai, Cyprus, Karachi, Qatar, Riyadh, Tashkent, and Warsaw, Amnesty said.