"What we can't do is simply turn away from our responsibilities to the security of the British people."
In a highly critical report, the joint parliamentary committee said there was now a "disturbing number of credible allegations" of British complicity in torture.
These allegations include the rendition and alleged abuse of British resident Binyam Mohammed from Pakistan to Morocco, prior to being taken to Guantanamo Bay.
The Metropolitan Police are investigating the role of one MI5 officer in Mr Mohamed's case.
Last week the High Court revealed that the same officer visited Morocco three times during the period that Mr Mohamed says he was being secretly tortured there.
'COMPLICITY' ALLEGATIONS
Binyam Mohamed: Claims to have been tortured in Morocco by interrogators who asked him questions about his life which he says could only have come from British authorities
Salauddin Amin: Claims Britain was complicit in alleged torture suffered following his arrest in Pakistan
Rangzieb Ahmed: Claims his fingernails were pulled by a Pakistani torturer and MI5 supplied Pakistani interrogators with questions
The committee also looked at other cases where British men, two of whom have been convicted of terror offences, say they were visited by British intelligence officers while they were detained and allegedly mistreated by Pakistani authorities.
But in all the cases, the parliamentary committee said it could not get to the facts because too many questions were not being properly answered.
It said that both the foreign secretary and home secretary, as well as the director general of MI5, had declined to give evidence on what was known about torture or mistreatment.
The ministers appeared "determined to avoid parliamentary scrutiny", said the report, and had batted away important questions with standardised answers.
Committee chairman Andrew Dismore MP said: "The allegations we have heard about UK complicity in torture are extremely serious.
"It is unacceptable both for ministers to refuse to answer policy questions about the security services, and for the director general of MI5 to answer questions from the press but not from a Parliamentary committee."
Revised guidance due
But foreign affairs minister Ivan Lewis insisted the foreign secretary had answered questions on torture allegations.
The prime minister has pledged to publish revised guidance to intelligence officers but Mr Dismore added: "General assertions of non-complicity are no longer an adequate response to the many detailed allegations.
A more obvious case of outsourcing of torture, a more obvious case of passive rendition, I cannot imagine
David Davis MP
"An independent inquiry is the only way to get to the bottom of these stories, clear the air and make recommendations for the future conduct and management of the security services.
"The recent allegations should be a wake-up call to ministers that the current arrangements are not satisfactory. We look to the government to respond positively to our recommendations and not to continue to hide behind their wall of secrecy."
Clive Baldwin, a senior legal adviser for Human Rights Watch, said a full public inquiry was needed because the "nature, level and rapidity" of allegations meant it was "something more than a one-off case".
Shadow foreign secretary William Hague said: "We also call on the government urgently to clarify what legally constitutes complicity in torture.
"All credible allegations of complicity in torture should be thoroughly investigated if public trust is to be restored."
Former shadow home secretary David Davis, who resigned his seat in protest over civil liberty issues, said the national security arguments had been "grotesquely misused".
"This is not simply a question of accepting intelligence, everyone accepts that if on one occasion or a couple of occasions, something turns up that tells you something is about to happen - it's actually got a name, the ticking bomb scenario - then you would be duty-bound to use that intelligence to the best of your ability.
"What this is, is about a policy of encouraging, of complicity, of involvement effectively in a pattern of torture and it's much, much more than just accepting the odd piece of intelligence."
A spokesman for the government rejected the call for an independent inquiry, saying that oversight was already sufficient.
"The government unreservedly condemns the use of torture as a matter of fundamental principle and works hard with its international partners to eradicate this abhorrent practice worldwide," said the spokesman.
"The government has already made clear it is committed to publishing guidance to intelligence officers as well as asking the Intelligence and Security Committee to consider new developments on detention and rendition."
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