In a joint letter to the solicitor for the inquiry, 10 groups including Liberty, Reprieve and Amnesty International said they did not intend to submit any evidence or attend any further meetings with the inquiry team.
It follows the publication of the inquiry's protocols which show the final decision on whether material uncovered by the inquiry, led by Sir Peter Gibson, can be made public will rest with the Cabinet Secretary.
The protocols also stated that former detainees and their lawyers will not be able to question intelligence officials and all evidence from current or former members of the security and intelligence agencies, below the level of head, will be heard in private.
In the letter, the campaigners wrote: "Plainly an inquiry conducted in the way that you describe and in accordance with the protocol would not comply with Article Three of the European Convention on Human Rights.
"We are particularly disappointed that the issue of what material may be disclosed to the public will not be determined independently of Government and, further, that there will be no meaningful participation of the former and current detainees and other interested third parties.
"As you know, we were keen to assist the inquiry in the vital work of establishing the truth about allegations that UK authorities were involved in the mistreatment of detainees held abroad.
"Our strong view, however, is that the process currently proposed does not have the credibility or transparency to achieve this.
"If the inquiry proceeds on this basis, therefore, and in light of indications from the lawyers acting for former detainees that they will not be participating, we do not intend to submit any evidence or attend any further meetings with the inquiry team."
The letter was signed by campaigners the Aire centre, Amnesty International, British Irish Rights Watch, Cageprisoners, Freedom from Torture, Human Rights Watch, Justice, Liberty, Redress and Reprieve.
A second letter written jointly by Imran Khan and solicitors who represent former Guantanamo Bay detainees also confirmed their intention to pull out.
"We consider it impossible to advise those whom we represent that the structure and protocols now confirmed for the Gibson inquiry can achieve what are essential ingredients for a public inquiry into grave state crimes," it said.
"What is proposed is a 'Detainee Inquiry' in which there will be no constructive participation by the detainees.
"The detainees will not be able to ask questions or see or hear the key evidence which is to be considered only in secret session.
"They will not even know if the individuals being questioned are the right ones."
They added that human rights obligations and international law for an inquiry "have been deliberately avoided".
The lack of input for detainees, "simply serves to demonstrate that there is no comprehension on the part of the Government of the gravity of the crimes which representatives of the state may have committed", they said.
"We had hoped as lawyers to assist in a transparent exercise of vital importance.
"It is a matter of profound regret that our assessment is that the inquiry does not provide the means by which this can be realised.
"In the absence of there being any alteration to the protocols, our advice is compelled to be that it is inappropriate for our clients to submit evidence."
A series of high-profile human rights lawyers signed the letter, including Louise Christian, Irene Nembhard, Gareth Peirce, Tayab Ali and Imran Khan.
Solicitor Gareth Peirce, who has signed the letter to the inquiry, represents 11 current or former Guantanamo Bay detainees.
Shami Chakrabarti, director of Liberty, said: "If this inquiry proceeds without the participation of the victims it will be nothing more than a waste of time and public money.
"Until a credible, independent process is established this shameful chapter of the war on terror continues.
"A year ago the Government accepted praise for the promise of a public inquiry - but the result, involving sidelining victims and a presumption of secrecy, is nothing of the kind."
Tim Cooke-Hurle, an investigator with Reprieve, added: "Since the torture inquiry was announced a year ago, we have tried repeatedly to make it work.
"It is frustrating that the Government has instead chosen to proceed with a secretive and toothless review.
"By ignoring the concerns of torture victims and major human rights organisations, the Government risks a pointless whitewash."
Prime Minister David Cameron announced the inquiry a year ago after claims that former Guantanamo Bay detainee Binyam Mohamed was tortured with the knowledge of the British security services while held by the CIA in Pakistan.
A number of other former detainees have since brought legal action against the UK Government, claiming they were subjected to similar mistreatment with the knowledge of MI5 or MI6.
Allegations have also been made of UK involvement in the extra-judicial transfer, or rendition, of terror suspects between countries since the 9/11 attacks on the US.
Last November, Justice Secretary Kenneth Clarke said secret payouts to 16 former detainees held at Guantanamo Bay were necessary to enable the security services to concentrate on protecting Britain and pave the way for the inquiry.
Weeks of negotiations led to a settlement which will avoid the need for protracted legal battles that could have run up a bill of £50 million over five years, Mr Clarke said.
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