Members of the foreign affairs committee of the House of Commons feel that the lack of information from the UK government has forced them to seek answers in the United States.
A report released by the committee today into human rights and the "extraordinary rendition" flights will express dissatisfaction with the lack of answers from Jack Straw, the Foreign Secretary, and Ian Pearson, the human rights minister, who were questioned by MPs as part of their inquiry.
It will intensify the pressure on Tony Blair to reveal the extent of the government's knowledge of the practice ahead of his No 10 press conference today.
Paul Keetch, a Liberal Democrat member of the committee, said: "We need to press ahead with a detailed inquiry into this, because the answers given to us so far by Jack Straw have been unsatisfactory."
Liberal Democrats have separately threatened to take ministers to the parliamentary ombudsman over their refusal to hand over details of flights passing through British military bases.
The fact-finding mission on torture flights will dominate the committee's annual trip across the Atlantic.
Committee members will meet with United Nations representatives in New York - who have demanded answers on the "torture" flights - and congressmen in Washington.
UN officials met British civil servants last year following allegations that the CIA had transported suspected terrorists to eastern European torture bases for interrogation.
The speculation was given credence by the National Air Traffic Control Service, which confirmed about 200 flights had passed through the UK over the past five years. However, yesterday, the Foreign Secretary again denied he had any knowledge of such flights.
"We know of no occasion where there has been a rendition through UK territory, or indeed over UK territory, nor do we have any reason to believe that such flights have taken place without our knowledge," Mr Straw said.
The Foreign Secretary has resisted the committee's demands to allow them to interview his officials, saying it was more a matter for the intelligence and security committee, which meets behind closed doors.
Pressure is also growing on other European Union countries to reveal details of the flights.
An investigation on the CIA secret prisons by the Council of Europe, led by Swiss senator Dick Marty, is due to report its findings to the European Parliament today.