The former cabinet minister Chris Huhne has called for an investigation into which Labour cabinet ministers signed off GCHQ's Tempora programme, the clandestine electronic surveillance programme revealed by leaks from the former US intelligence contractor Edward Snowden.

Huhne, the Liberal Democrat who resigned from parliament after being jailed over lying about a speeding offence, has revealed the cabinet was not informed about Tempora, which was tested in 2008 and fully implemented in 2011.

Writing in the Guardian, the former member of the coalition's national security council asks whether the Labour cabinet was similarly kept in the dark and suggests the decision to authorise the programme could yet be made subject to judicial review.

He speculates that Labour's relative silence on the issue may have been prompted by the fact that the programme could have been signed off by the former Labour foreign secretary David Miliband, brother of Ed Milband.

Huhne writes: "If it was David Miliband, this may well explain why the Labour frontbench has been so muted. Though Ed Miliband has been happy to admit past Labour errors on Murdoch and other matters, his appetite for political fratricide may be sated."

The Tempora programme – revealed in the cache of documents leaked by Snowden – extracts and processes data from fibre optic cable communications. The data is preserved for three days while metadata is kept for 30 days.

GCHQ comes under the joint ministerial oversight of the foreign secretary and the prime minister. David Cameron has not denied that he failed to inform cabinet members of GCHQ's new technological powers, but said they were free to ask questions of GCHQ.

With some Conservative MPs planning in a parliamentary debate this week to make the case for the prosecution of the Guardian over the Snowden disclosures, the US ambassador to Britain, Matthew Barzun, rejected an opportunity to criticise the newspaper on Sunday, saying he wanted to focus on the importance of the debate about the tradeoffs between security and privacy.

Barzun, appearing on the BBC's Andrew Marr Show for the first time since his arrival in London in June, talked about the impact of the debate on national security created by Snowden's leaks. He also stressed President Barack Obama was clear that his response to the leaks should not have "a chilling effect on the press".

Asked if he shared the UK security services' concerns about the threat to national security from the leaks, he said he wanted to focus on the "importance of having this debate about what the tradeoffs are between security and privacy, between transparency and secrecy, and to do so in a way that protects whistleblowers – which is different, by the way, from wholesale releasing of information, hundreds of thousands of documents".

Barzun said Obama had "promised to seek to balance the legitimate security concerns of not only our citizens but of our allies, and balance those with the privacy concerns shared by all people". He said the president "put in specific measures to protect whistleblowers if they see something illegal or unethical. That's an important part of the balance."

Harold Evans, the former editor of the Sunday Times and the Times, has come to the defence of the Guardian for its reporting of the Snowden leaks.

"No editor in his right mind wants to give aid to murderous enemies," he writes, "but every editor is duty bound to scrutinise the use of power, responsibly but fearlessly, however personally unappealing a leaker may be. Conflict between the conceptions of duty is inevitable, indeed healthy. Reporting often exposes an ill that government has not recognised or acknowledged."

Huhne argues the decision to go ahead with the Tempora programme could have been sanctioned by Jack Straw, the foreign secretary from June 2001 to May 2006, but it is more likely to have been agreed by Margaret Beckett, foreign secretary from May 2006 to June 2007, or David Miliband, who had the role from June 2007 to the general election in May 2010. Trials for the programme started in 2008 in Bude, Cornwall.

Labour has, since June, consistently sought ministerial reassurance that GCHQ has been operating under proper ministerial oversight, but has not treated the issue as a major campaign priority, as it does battle on mainstream cost of living issues.

The Lib Dems have promised a review of the law and the quality of oversight of the intelligence agencies by ministers and parliament.

Huhne says he is sure GCHQ would not have pressed ahead with the multi-million-pound programme without the agreement of ministers. He writes: "I discount the possibility that GCHQ went rogue. GCHQ's head at the time, Sir David Pepper, was a bureaucratic stickler. Sir David Omand, Cabinet Office permanent secretary in charge of intelligence, would also have insisted on ministerial signoff. So which prime minister and foreign secretary were responsible?"

He adds: "If the Home Office thought that a full-scale parliamentary act was necessary to take similar powers for the police – the communications data bill – questions have to be asked about the reasons GCHQ thought it had a legal basis for its activity."

Huhne argues: "The question of how these programmes were authorised are of constitutional importance, but none of them has been asked, let alone answered."

He suggests that if parliament is not willing to investigate the authority for these decisions, then it may be necessary to rely on the law.

The pressure group Liberty has already agreed to take a case to the Investigatory Powers Tribunal to see if warrants were properly issued under the Regulation of Investigatory Powers Act passed 13 years ago, before the technology was developed. There is little expectation that the case will reveal much due to the tight criteria under which the tribunal operates.

Huhne instead suggests the case could be subject to a judicial review. He cites Lord Macdonald QC, the former director of public prosecutions, saying: "The question is whether the government had proper lawful authority for what they have done. It is potentially a subject for judicial review."

Huhne says: "There is an overwhelming democratic interest in testing whether that decision was ultra vires – outside legal powers voted by parliament.

"There is normally a three-month time limit with judicial review, but that should not be an impediment when the powers continue to be used and when the original decision was secret. The Snowden revelations show an executive arm snatching exaggerated powers with no public debate or parliamentary approval. For the sake of our freedoms, but also our democracy, this needs to be put right."