The United States is operating "floating prisons" to house those arrested in its war on terror, according to human rights lawyers, who claim there has been an attempt to conceal the numbers and whereabouts of detainees.

Details of ships where detainees have been held and sites allegedly being used in countries across the world have been compiled as the debate over detention without trial intensifies on both sides of the Atlantic. The US government was yesterday urged to list the names and whereabouts of all those detained.

Information about the operation of prison ships has emerged through a number of sources, including statements from the US military, the Council of Europe and related parliamentary bodies, and the testimonies of prisoners.

The analysis, due to be published this year by the human rights organisation Reprieve, also claims there have been more than 200 new cases of rendition since 2006, when President George Bush declared that the practice had stopped.

It is the use of ships to detain prisoners, however, that is raising fresh concern and demands for inquiries in Britain and the US.

According to research carried out by Reprieve, the US may have used as many as 17 ships as "floating prisons" since 2001. Detainees are interrogated aboard the vessels and then rendered to other, often undisclosed, locations, it is claimed.

Ships that are understood to have held prisoners include the USS Bataan and USS Peleliu. A further 15 ships are suspected of having operated around the British territory of Diego Garcia in the Indian Ocean, which has been used as a military base by the UK and the Americans.

Reprieve will raise particular concerns over the activities of the USS Ashland and the time it spent off Somalia in early 2007 conducting maritime security operations in an effort to capture al-Qaida terrorists.

At this time many people were abducted by Somali, Kenyan and Ethiopian forces in a systematic operation involving regular interrogations by individuals believed to be members of the FBI and CIA. Ultimately more than 100 individuals were "disappeared" to prisons in locations including Kenya, Somalia, Ethiopia, Djibouti and Guantánamo Bay.

Reprieve believes prisoners may have also been held for interrogation on the USS Ashland and other ships in the Gulf of Aden during this time.

The Reprieve study includes the account of a prisoner released from Guantánamo Bay, who described a fellow inmate's story of detention on an amphibious assault ship. "One of my fellow prisoners in Guantánamo was at sea on an American ship with about 50 others before coming to Guantánamo ... he was in the cage next to me. He told me that there were about 50 other people on the ship. They were all closed off in the bottom of the ship. The prisoner commented to me that it was like something you see on TV. The people held on the ship were beaten even more severely than in Guantánamo."

Clive Stafford Smith, Reprieve's legal director, said: "They choose ships to try to keep their misconduct as far as possible from the prying eyes of the media and lawyers. We will eventually reunite these ghost prisoners with their legal rights.

"By its own admission, the US government is currently detaining at least 26,000 people without trial in secret prisons, and information suggests up to 80,000 have been 'through the system' since 2001. The US government must show a commitment to rights and basic humanity by immediately revealing who these people are, where they are, and what has been done to them."

Andrew Tyrie, the Conservative MP who chairs the all-party parliamentary group on extraordinary rendition, called for the US and UK governments to come clean over the holding of detainees.

"Little by little, the truth is coming out on extraordinary rendition. The rest will come, in time. Better for governments to be candid now, rather than later. Greater transparency will provide increased confidence that President Bush's departure from justice and the rule of law in the aftermath of September 11 is being reversed, and can help to win back the confidence of moderate Muslim communities, whose support is crucial in tackling dangerous extremism."

The Liberal Democrat's foreign affairs spokesman, Edward Davey, said: "If the Bush administration is using British territories to aid and abet illegal state abduction, it would amount to a huge breach of trust with the British government. Ministers must make absolutely clear that they would not support such illegal activity, either directly or indirectly."

A US navy spokesman, Commander Jeffrey Gordon, told the Guardian: "There are no detention facilities on US navy ships." However, he added that it was a matter of public record that some individuals had been put on ships "for a few days" during what he called the initial days of detention. He declined to comment on reports that US naval vessels stationed in or near Diego Garcia had been used as "prison ships".

The Foreign Office referred to David Miliband's statement last February admitting to MPs that, despite previous assurances to the contrary, US rendition flights had twice landed on Diego Garcia. He said he had asked his officials to compile a list of all flights on which rendition had been alleged.

CIA "black sites" are also believed to have operated in Thailand, Afghanistan, Poland and Romania.

In addition, numerous prisoners have been "extraordinarily rendered" to US allies and are alleged to have been tortured in secret prisons in countries such as Syria, Jordan, Morocco and Egypt.