Claims by two Muslims accused of role in bomb attack during 2010 World Cup date from after coalition came to power

Two men facing terrorism charges in east Africa are accusing the British government and its intelligence agencies of being involved in their abduction, unlawful rendition and torture.

The allegations by Habib Suleiman Njoroge and his brother Yahya Suleiman Mbuthia closely echo those reported in the Guardian last year by a third terrorism suspect, Omar Awadh Omar.

The high court in London has given all three men permission to seek disclosure of British government documents that would support their claim that the UK was involved in their alleged mistreatment. Njoroge and Omar have also been given permission to seek documents relating to their rendition at a hearing at the high court in London this week.

During proceedings in the Ugandan courts, the men alleged British and American intelligence officers beat and punched them, hooded them, threatened them with firearms and told them they were to be flown to Guantánamo Bay. In response, the Ugandan government denied the men were mistreated, but said "the nature of the terrorist attacks necessitated joint investigations, by Ugandan police with foreign security officers, which included joint interrogations".

The trio's allegations date from August and September 2010, several months after the coalition government was formed. They come despite attempts by ministers to distance themselves from the torture and rendition scandals that dogged the previous Labour government, while also expressing clear support for the country's intelligence agencies.

Njoroge and Mbuthia were among a number of Kenyan Muslims detained in 2010 and taken to Uganda for questioning about two suicide bomb attacks on crowds of people watching World Cup football matches in July of that year. The Somali militant group al-Shabaab claimed responsibility for the attacks that killed 79 people and injured 70.

According to a report submitted to the United Nations security council last year, Omar, Njoroge and Mbuthia were linked by telephone records to a mobile phone that was attached to a third suicide bomb vest, which failed to explode. Kenyan media reports have claimed Omar was a leading figure in the bomb plot. All three men deny any involvement.

Omar was kidnapped in broad daylight in a Nairobi shopping centre and driven across the border to Uganda, where he says British and American interrogators were waiting for him. Omar says one of his interrogators, an Englishman who called himself Frank, became particularly angry and began stamping on his bare feet while asking him about two British Muslims who had been arrested in Nairobi.

Njoroge, a radio presenter from Mombasa, was arrested in September 2010, interrogated by Kenyan police and then allegedly driven while hooded and shackled to the Ugandan border to be handed over to that country's Rapid Response Unit (RRU), a police body whose use of torture has been documented by human rights groups.

While in RRU custody, Njoroge says he was kept naked, beaten, sexually assaulted and forced to sign a statement in which he confessed to being involved in the bombings. Among the officials interrogating him, he says, were men with American and British accents.

Mbuthia's complaint that he had been rendered from Kenya to Uganda a few days before his brother is not contested by the Ugandan authorities. He was dragged from a bus in Nairobi, hooded and handcuffed and driven to the border, where he says he was beaten and threatened with execution by RRU officers.

He says that, after being deprived of food and liquid for three days, he was interrogated by FBI officers who beat him, pointed firearms at him and threatened to shoot him if he refused to testify against Omar. During subsequent interrogation sessions, he says, the Americans were joined by a man with a Scottish accent.

The high court has concluded that there is a case to be made that the British government "would have been aware that there was evidence over many years that the RRU used illegal methods and severely mistreated those in its custody" during interrogation.

Asked about the claims, a Foreign Office spokeswoman said: "The UK government's policy is clear: we do not participate in, solicit, encourage or condone the use of torture or cruel, inhuman and degrading treatment or punishment for any purpose. We have consistently made clear our absolute opposition to such behaviour and our determination to combat it wherever and whenever it occurs. We cannot comment on ongoing legal cases."

Omar, Njoroge and Mbuthia's UK lawyers are pursuing similar arguments to those deployed on behalf of Binyam Mohamed three years ago, during litigation that exposed MI5's complicity in his torture in Pakistan and Morocco, and which resulted in one of the country's most senior judges condemning the agency's officials for their "dubious record" over those abuses.

The allegations are resulting in the sort of court cases that would be heard behind closed doors under controversial new secrecy proposals drawn up by Ken Clarke's Ministry of Justice, in consultation with MI5 and MI6.

Under those plans, ministers would be able to decide that evidence they considered too sensitive to be aired in public during civil trials – including trials in which they themselves are defendants – could be concealed from the public, the media and even the claimants.

The same green paper contains proposals to prevent claimants from making use of the legal doctrine that has been employed by lawyers representing the three men during efforts to force the government to disclose any documentary evidence that shows it was involved in their rendition and mistreatment.

After parliament's human rights committee published a damning report about the proposals, deputy prime minister Nick Clegg warned cabinet colleagues that they were unacceptable in their current form.

In a major speech last November on the work of the agencies, William Hague, the foreign secretary, said the coalition was "drawing a line under the past". Hague stressed, however, that he was obliged to grapple with "the most difficult ethical and legal questions".

East Africa has been of growing concern to US and UK intelligence agencies, who say that about 200 foreigners have travelled to Somalia to train and fight with al-Shabaab. Leon Panetta, the US defence secretary, describes the US military base at Camp Lemonnier in neighbouring Djibouti as "the central location for continuing the effort against terrorism". Despite an increase in military aid to neighbouring countries, Jonathan Evans, the director general of MI5, has said he is "concerned that it is only a matter of time before we see terrorism on our streets inspired by those who are today fighting alongside al-Shabaab".

British concerns were heightened by initial reports that a young British Muslim from London had a hand in the suicide bomb attacks, although it is thought that MI5 and MI6 no longer believe this to be the case. This individual has since been reported to have been killed in Somalia. A significant number of other British Muslims are reported to have travelled to the region to join up with al-Shabaab, and many are thought to have travelled through Kenya.