The US government is attempting to halt a lawsuit that could establish whether any of the Central Intelligence Agency's so-called rendition flights have been partly planned on British soil. Lawyers representing a number of men who have been held at Guantánamo are suing Jeppesen Dataplan, a subsidiary of the Boeing Corporation, accusing Jeppesen of involvement in the flights that took the men to secret prisons around the world. Once there, the men say, they were tortured.

The lawyers say they strongly suspect that at least some of the logistic support for the CIA's flights was arranged at Jeppesen's office in Crawley, West Sussex, a few miles from Gatwick airport.

However, the US government is asking a federal court to dismiss the lawsuit because "to proceed would risk the disclosure of highly classified information" about the agency's methods.

According to Washington's arguments, that information would include "whether any private entities or other countries assisted the CIA", as well as the locations of any secret prisons and "the methods of interrogation employed".

The men's lawyers at Reprieve, a London-based legal charity, say that if the case is dismissed, they may sue Jeppesen for damages in the English courts.

Reprieve is seeking unspecified damages on behalf of six men, including Benyam Mohammed, an Ethiopian national who grew up in Notting Hill, west London, who was first arrested in Pakistan before being flown to Morocco on a flight allegedly facilitated by Jeppesen. In Morocco he was subjected to severe physical and psychological torture, according to Reprieve's complaint. "He was routinely beaten, suffering broken bones and, on occasion, loss of consciousness due to the beatings. His clothes were cut off with a scalpel and the same scalpel was then used to make incisions on his body, including his penis. A hot stinging liquid was then poured into open wounds on his penis where he had been cut. He was frequently threatened with rape, electrocution, and death."

Another plaintiff is Bisher al-Rawi, an Iraqi citizen who had lived in Britain for 19 years when arrested in the Gambia in 2002, and who was freed from Guantánamo last March after it emerged that he had acted as a go-between for MI5 and the radical cleric Abu Qatada. Rawi says he was flown to Afghanistan, where he was "punched and badly beaten", deprived of food, warmth or light, and subjected to loud noise around the clock.

According to Jeppesen's publications, its international trip planning services are arranged by two offices, with San Jose in California managing the western hemisphere, and Crawley managing the eastern hemisphere. Papers filed by Reprieve and the American Civil Liberties Union at a US district court in San Jose say that "publicly available records demonstrate that Jeppesen facilitated more than 70 secret rendition flights over a four-year period to countries where it knew or reasonably should have known that detainees are routinely tortured or otherwise abused".

Last June, Dick Marty, a Swiss senator who investigated the CIA's use of European territory and airspace during prisoner operations, also concluded in his report to the Council of Europe that Jeppesen had falsified flight plans.

A spokesman for Jeppesen said: "We manage the logistics and planning of international operations for thousands of organisations and people operating aircraft. It is not necessary for us to know the specific nature of a customer's flight. In the event that we learn something about the purpose of a flight, our customers have the reasonable expectation that it will be held in confidence." Clive Stafford Smith, legal director of Reprieve, said: "There seems to be little doubt that these rendition flights were planned on British soil. The US government has intervened to prevent their dirty laundry from being washed in public, which is reprehensible."