There is growing pressure from MPs for ministers to shed light on claims that the CIA has used UK airports to move suspects to other nations for torture.
Campaigners are demanding police investigate the claims
A new all-party group on "extraordinary renditions" will meet on Monday. Its leaders accuse the government of evading key questions on the issue.
Foreign Secretary Jack Straw has written to the US on behalf of the EU asking about alleged "secret prisons".
The UK says it is not aware of British land being used for "torture" flights.
The new group of MPs has been formed by Conservative Andrew Tyrie, former Labour minister Chris Mullin and Liberal Democrat foreign affairs spokesman Sir Menzies Campbell.
Mr Tyrie told BBC Radio 4's Today programme he was surprised by the number of MPs who said they would join the group.
Many people were worried that the UK might be condoning torture, he said.
The group's main job would be to collect information, he said, because the government was making it very difficult to find out what was happening.
He accused the Foreign Office of producing "obfuscation and carefully worded replies" to his questions.
Mr Tyrie said he had been told records of transit applications were not kept.
"There is quite a lot of evidence to suggest that something is going on, that there are flights taking place to countries where they can be tortured," he said.
The UK should be enforcing the law and the United Nations convention against torture, he argued.
"We are trying to win over the hearts and minds of millions of people in the Middle East, saying that we have got a better way of doing things and at the same time we seem to be sinking to the very standards that we have been criticising," added Mr Tyrie.
Police inquiry calls
Civil rights group Liberty has written to several chief constables demanding they investigate claims that CIA flights stopped at UK airports.
The airports allegedly involved include Biggin Hill in Kent, Birmingham, Bournemouth, RAF Brize Norton in Oxfordshire, Farnborough, Gatwick, Heathrow, Luton, Mildenhall in Suffolk, RAF Northolt in north London, Stansted and Prestwick.
Former Foreign Office legal adviser Elizabeth Wilmshurst said the UK had a duty to investigate any allegations of torture on its territory.
A Foreign Office spokesman said: "We are not aware of the use of UK territory or airspace for the purpose of extraordinary rendition, nor have we received any requests, nor granted any permission for the use of UK territory or airspace for such purposes."
Mr Straw has said he expressed concern about the claims about secret prisons on EU territory in his letter to US Secretary of State Condoleezza Rice.
The US government has said its laws have not been broken.
But it has refused to confirm or deny the existence of "secret prisons" in third countries.