The coalition government should "leave no stone unturned" in the search for the truth about the UK's complicity in foreign torture, the head of Amnesty International has said.

An inquiry promised by William Hague, the foreign secretary, needs to be both independent and able to decide whether any individuals should be prosecuted, said Amnesty's interim secretary general, Claudio Cordone.

"We look forward to an inquiry that is truly independent and looks not only at potential criminal responsibility but also at Britain's co-operation agreements with the United States and other countries," said Cordone. "It should leave no stone unturned."

Launching its annual human rights report, Amnesty was highly critical of the last Labour government for "stonewalling" in the face of repeated calls for an independent investigation into the mounting allegations that UK intelligence officials were complicit in abductions, illegal detention and torture since the al-Qaida attacks of September 2001.

The organisation said it was also concerned about the UK relying on "diplomatic assurances" when carrying out deportations to countries such as Algeria and Jordan.

In London, Amnesty's UK campaigns director, Tim Hancock, said Britain had lost the moral high ground in recent years, and that the new political era offered an opportunity for the UK to break free of the human rights abuses of the past.

"Both parties in the new government have criticised the previous government on human rights grounds and it's vital that they live up to their fine words now they're in office," Hancock said.

"We're stressing that 'justice gaps' – where people are cut off from accessing justice – need to be closed all around the world, and it's only right that the UK delivers on law and order at home and abroad. While dozens of countries in the world have very poor human rights records, the truth is that ours has been nothing to write home about either."

The Foreign Office was taken by surprise last Thursday when Hague said that an investigation would be held, and Whitehall officials later insisted that any such inquiry could not start while a number of court cases are ongoing. Several men who allege UK complicity in their rendition and torture are currently suing MI5, MI6 and the British government.

The same officials said that any inquiry would need to be held in secret – a proposal that has been condemned by human rights groups.

Those organisations say the inquiry should establish:

• who authorised the bilateral agreements with the US that led to Britain offering logistic support for the CIA's rendition programme of kidnap and torture, and whether any other agreements led to human rights abuses;

• who authorised the secret interrogation policy, transmitted to MI5 and MI6 officers, telling them they could interrogate people who were being tortured, as long as they did not participate and were not "seen to condone it";

• what Downing Street knew about the torture of Binyam Mohamed, and about the torture of several British citizens since 2001;

• and what the last foreign and home secretaries, David Miliband and Alan Johnson, knew about the UK's involvement in torture and rendition.

Amnesty's annual report for 2010, covering 159 countries, condemned a number of influential nations that it says attempt to stand above human rights laws. It accused these countries, including the US, Russia and China, of shielding allies from criticism and only taking action when it is politically convenient.

The organisation also criticised the EU for failing to live up to its commitments on human rights, citing the tolerance of the CIA's rendition flights and secret detention program. It added that several European countries had repeatedly violated rulings by the European court of human rights against the return of terror suspects to countries where they are at risk of torture.

Amnesty also recorded torture, unfair trials and restrictions on free speech in dozens of countries, singling out Saudi Arabia, Iran, China, North Korea, Myanmar, Russia and Sri Lanka for criticism.