Ministers are failing to meet their legal duties to investigate claims that the CIA is flying terror suspects through the UK, say MPs and peers.
There are claims CIA flights have landed around the UK
Parliament's joint committee on human rights says the government should take "active steps" to find out more details about certain flights.
The appeal comes in a damning report which also accused the UK of trying to undermine the absolute ban on torture.
The government insists there is no evidence of secret prisoner flights.
But allegations about the so-called "renditions" have continued.
And the committee says it should require chartered civil aircraft to provide staff and passenger lists when they use UK airports or fly through British airspace.
Such steps are not only allowed under UK law but also needed to ensure the government complies with the convention on torture, it said.
A committee spokesman said the report concluded that the "government has not adequately demonstrated that it has satisfied the obligation under domestic and international human rights law to investigate credible allegations of renditions".
That was a concern echoed by Conservative MP Andrew Tyrie, who chairs the all-party Parliamentary Group on Extraordinary Rendition, who said he had not been reassured by comments made by Jack Straw back in December.
The former foreign secretary said had failed to identify any request from the Bush administration for the passage through Britain of aircraft taking terrorist suspects to interrogation centres.
Mr Tyrie said: "First of all I'm not suggesting Jack Straw lied, but all he's done is a paper search of some files.
"In another response to a parliamentary question from me he said that after renditions are completed the papers are generally destroyed, it's hardly surprising that he can't find anything in his files.
"What we need is much more than just shuffling around in filing cabinets from the government.
"We need the government to ask the US government what's really been going on."
The report says the UK government's response to the calls will determine whether a public inquiry into the controversy is needed.
It also accused ministers of trying to undermine the absolute ban on torture.
The committee criticises the government for joining with other countries to challenge a European court judgement from the 1990s which says people cannot be deported to a country where they face a real risk of torture.
The UK is joining Slovakia, Lithuania and Portugal in a case about whether the Netherlands can deport somebody to Algeria despite claims they could be tortured.
The report voices concern the case "may send a signal that the absolute prohibition of torture may in some circumstances be overruled by national security considerations".
It says there can be no "balancing exercise" between security and risk of torture.
The committee also attacks the government's attempts to reach diplomatic agreements with some countries so they can deport terror suspects without fear they will be tortured.
It says it has "grave concerns" after examining the agreements already signed with Libya, Lebanon and Jordan.
"The government's policy of reliance on diplomatic assurances against torture could well undermine well-established international obligations not to deport anybody if there is a serious risk of torture or ill-treatment in the receiving country," it says.
Relying on the agreements could create "a substantial risk of individuals actually being tortured", which would mean the UK had broken its human rights treaty obligations.
The Foreign Office said it would carefully consider the report and give a formal response in due course.