Britain's three senior spy chiefs came into the public glare for the first time to claim that leaks by the former NSA analyst Edward Snowden were being "lapped up" by the country's adversaries, but also to concede that the disclosures had prompted discussion with the government over how to be more transparent about their methods.

Despite an often gentle first public cross-examination of the heads of MI5, MI6 and GCHQ, some members of the intelligence and security committee, including the former head of the civil service Lord Butler, expressed their concern at the legal oversight of the intelligence agencies.

Butler said it was hardly credible that the legislation governing the agencies was "still fit for purpose for the modern world". After the session, Sir Menzies Campbell, a Liberal Democrat member of the ISC, also called for a review of the law, "not least to provide the public with a sense of reassurance and confidence that there is a substantial legal framework".

A third ISC member, the Tory MP Mark Field, also revealed that members felt they had not been told about the intricacies of GCHQ's capabilities, demanding in private "at the earliest opportunity a comprehensive update on collaborations that are taking place with overseas intelligence agencies" – including, by implication, the US National Security Agency. Sir Iain Lobban, the head of GCHQ, agreed to do so.

The 90-minute session came most alive when the spy chiefs expressed their cold fury at the Edward Snowden disclosures in the Guardian and other papers, claiming that they would lead for years to an "inexorable darkening" of their knowledge of those threatening the country.

Sir John Sawers, head of MI6, said: "The leaks from Snowden have been very damaging. They have put our operations at risk. It is clear our adversaries are rubbing their hands with glee. Al-Qaida is lapping it up."

Lobban told MPs there had been a gradual but inexorable deterioration of GCHQ's knowledge of its targets after five months of near daily chat by potential terrorists about how to adapt their methods of communication in the light of the disclosures about GCHQ's modus operandi. He asserted: "The cumulative effect of the media coverage, the global media coverage, will make the job that we have far, far harder for years to come." Success, he in effect argued, required Britain's enemies to be unaware or uncertain of GCHQ's methods. He added: "There is a complex and fragile mosaic of strategic capability which allows us to discover, to process, to investigate and then to take action. That includes terrorist cells, it reveals people shipping secrets or expertise or materials to do with chemical, biological, nuclear around the world. It allows us to reveal the identities of those involved in online sexual exploitation of children. Those people are very active users of encryption and of anonymisation tools. That mosaic is in a far, far weaker place than it was five months ago."

Neither Sawers nor Lobban was willing to give the committee any specific detail about the compromise of intelligence capability in public, but they promised to be "very, very specific" in a future private session.

Lobban also expressed fears that he was going to lose the co-operation of internet service providers in conducting telephone and internet monitoring. "I am concerned about the access that we can lawfully require of communications companies, which is very difficult if they are based overseas," he said.

He hotly denied that GCHQ delved into "innocent emails and calls", but said the agencies needed to have access to "the enormous hayfield" if they were to find the needles.

Lobban promised: "We do not spend our time listening to the telephone calls or reading the emails of the majority, the vast majority – that would not be proportionate, it would not be legal. We do not do it. We can only look at the content of communications where there are very specific legal thresholds and requirements which have been met. So that's the reality. We don't want to delve into innocent emails and phonecalls."

But the GCHQ boss said there were some people who would be monitored, and it was the job of the intelligence agency to monitor "a terrorist, a serious criminal, a proliferator, a target or if your activities pose a genuine threat to the national or economic security of the UK".

On Thursday night, one of the members of the ISC said that the committee knew GCHQ was able to secretly access vast quantities of data. Labour's former counter-terrorism minister Hazel Blears told BBC's Newsnight that the ISC was fully aware of "what they were doing in terms of being able to collect information".

Former cabinet minister Chris Huhne had said top government figures were kept in the dark about GCHQ's ability to access data, in an operation codenamed Tempora. But in what appears to be the first admission to the contrary, Blears said: "The committee did have a broad understanding of what the capabilities of GCHQ were."

Pressed on whether it had been aware of the existence of the Tempora programme, she said: "We didn't know the names of these projects, and I'm sure the exact same situation applies in America. But in terms of broad capabilities, yes we did," said Blears.

"We have been looking at them now for several years, we have been on several visits to GCHQ, we've had very, very confidential briefings about what the capabilities were and obviously we were satisfied that they were operating within our legal framework."

At Thursday's hearing, Sawers criticised newspapers for claiming they could judge whether disclosures would compromise national security, saying they were not particularly well placed to make such decisions. But pressed to accept that the disclosures had raised issues about the line between secrecy and openness, however, Lobban acknowledged the urgency of the issue, saying: "Clearly with the situation we are in, we are actively considering that with government."

The spies used their public outing to defend their £2bn budget, and to claim that the security threat facing Britain was growing. Andrew Parker, director of MI5, said that since 2005 and the 7/7 attacks, 34 separate plots had been foiled, including one that would have created mass casualties.

He said the numbers sympathetic to violent extremism were in the low thousands, saying "terrorism tourism" was now a serious problem as Britons, numbered in the low hundreds, travelling to fight in Syria had made the crisis worse.

Sawers also rejected allegations that intelligence agencies had been complicit in torture or have mistreated individuals. Parker added: "We do not participate in, incite, encourage or condone mistreatment or torture, and that is absolute."

A spokesperson for Guardian News and Media, publisher of the Guardian, said: "We welcome the fact that the intelligence chiefs acknowledged that they need to be more open as a result of the Snowden disclosures, but were surprised that unlike in the US and Europe there was no substantive discussion at all about anything Snowden revealed."