Britain's intelligence chiefs may have exaggerated the threat posed to national security by the leaking of the NSA files, according to a former lord chancellor who has questioned whether the legal oversight of MI6, MI5 and GCHQ is "fit for purpose".

Lord Falconer of Thoroton said he was sceptical of the claim by the heads of GCHQ, MI6 and MI5 that the leaks represent the most serious blow to their work in a generation, and warned that the NSA files highlighted "bulk surveillance" by the state.

Falconer, who also said he deprecated attempts to portray the Guardian as an "enemy of the state", pointed out that 850,000 people had access to the files leaked by the US whistleblower Edward Snowden.

Falconer, a close ally of Tony Blair who served as lord chancellor from 2003-07, told the Guardian: "I am aware that the three heads of the agencies said what has been published has set back the fight against terrorism for years. Sir John Sawers [the chief of MI6] said al-Qaida would be rubbing their hands with glee. This is in the context of maybe 850,000 people literally having access to this material."

Falconer, who is in charge of Ed Miliband's preparations for government, added: "It seems to me to be inconceivable that the intelligence agencies in the US and the UK were not aware that it would not be possible to keep secret these sorts of broad issues for any length of time. If the position was that the USA and the UK were intending to keep the general points I have been talking about secret then that seemed to me to be a very unrealistic position.

"Although I take very seriously what they say [about the importance of secrecy] I am sceptical that the revelations about the broad picture have necessarily done the damage that is being asserted."

In his Guardian interview Falconer, who described himself as a strong supporter of the intelligence agencies from his time working with them during his decade in government:

• Warned of "very, very serious questions" about whether the law has kept up with the rapid pace of technological change which has permitted what he describes as "bulk surveillance".

• Hit out at the former Tory defence secretary Liam Fox, who has written to the new director of public prosecutions, Alison Saunders, to ask her to assess whether the Guardian has breached counter-terrorism laws by publishing details from the leaked files.

Falconer said: "I think it is thoroughly wrong that, in the light of the disclosures that have been made, the Guardian is being treated in a similar way to an enemy of the state. Far from being an enemy of the state an organ like the Guardian, or indeed the New York Times, is part of the functioning of our democracy that makes the state as strong as it is."

• Praised the Guardian and the New York Times, which have formed a partnership to report on the leaked files, for working in a responsible way by alerting the agencies before publication. "From all that I can see the Guardian and the New York Times have taken immense trouble to avoid any individual operative or operation being endangered." The Guardian has spoken to the NSA and GCHQ before publishing details from the leaked files.

Falconer is one of the most senior figures to question the account given by the intelligence chiefs this month to parliament's intelligence and security committee (ISC). Sawers told the committee that the Snowden leaks had put operations at risk, adding that Britain's adversaries were "rubbing their hands with glee".

The Sunday Times quoted a Tory MP describing the joint appearance by Sawers, the GCHQ director, Sir Iain Lobban, and the MI5 director general, Andrew Parker, as a "total pantomime" after it emerged that they were told of questions in advance as part of a secret deal with the committee.

Lobban told the committee that his agents collect, though do not intercept, "innocent communications from innocent people" when they gather what he called the "haystack" of metadata.

Falconer said: "The material which has been revealed through the Snowden revelations about the NSA raises very, very serious questions about whether or not the United Kingdom's legal framework for oversight of the intelligence services' work in relation to the interception of communications and the obtaining of communications data from mobile telephone and other providers is fit for purpose."

Falconer, who spoke out in August against the detention of David Miranda, the partner of the then Guardian journalist Glenn Greenwald, under anti-terror laws, said he was struck by the intervention during the ISC hearing by the former cabinet secretary Lord Butler of Brockwell. Butler asked whether the Regulation of Investigatory Powers Act (Ripa) of 2000 is still "fit for purpose" given that technology has moved on so rapidly in the last 13 years.

Falconer said: "If you look at the codes of practice and the Ripa 2000 act, they both proceed on the basis that the warrant issued by the secretary of state for interception – ie listening in or looking at emails, their content – will be based upon individual cases. The agencies' right to get metadata about communications is also, I think, to be done on an individual basis even though no warrant is required.

"What the NSA data reveals is in effect bulk – and I use this word advisedly – surveillance. What the agency chiefs were saying to the ISC appeared to be in relation to that communications data: it is the way that we create the haystack within which we look for the needle.

"It may well be that the way that that is policed is adequate. But the current arrangements involve there being no decider other than the agencies as to what communications data shall be sought from servers and mobile telephone providers. In particular there is no warrant required from a secretary of state and there is no judicial permission given, albeit that the judge responsible for looking at the intelligence services generally will look at it on an annual basis."

Falconer said that three changes should be considered:

• The publication of goals from the agencies to allow applications for communications data or interception warrants to be judged against the goals.

• A new body – a judge or a minister – to give "consent to massive communications data exchange". Falconer said Britain should consider replicating the foreign intelligence court (Fisa) which oversees surveillance in the US.

• Handing powers to approve interception – as opposed to communications data – to the interception commissioner. This would strip the home secretary and foreign secretary of these powers.

Falconer said he was alarmed by attempts to portray the Guardian as an enemy of the state after Miranda's detention and by calls for prosecutions and attacks on the Guardian for endangering operations. He said: "I completely understand why the agency chiefs are keen that there should be appropriate confidentiality. I completely support them in relation to that. But I really deprecate the way the Guardian is being treated as the enemy of the state. That is not the right way to look at it.

"A reputable media outlet like the Guardian should be regarded as part of the landscape within which the agencies operate.

"And to abuse it publicly and to use the powers to be used against terrorists against it I think weakens the ability of our state to deal with change."

Asked about Fox's call for the CPS to investigate the Guardian, Falconer said: "We need to trust the media more. If the response of the state is immediately to go into criminal investigation mode then you chill badly investigations like this.

"I don't want to encourage people to break their obligation to the state – ie those who are employed by the state. But I think you have got to recognise that where there is an issue such as this where there has been a fundamental change in technology leading to the question of whether or not the balance is right between the ability to intrude and the need to protect the state – that is plainly a legitimate area for journalistic endeavour."

Falconer stressed that he strongly supports the work of the intelligence agencies. "I am a supporter of the intelligence services. I understand their importance and centrality to fighting terrorism.

"When I dealt with them as a minister I was always impressed by them." He said politicians and the media should support them in two senses – accept their importance in fighting terrorism and properly protect their operations.