Labour will on Monday propose substantial changes to the oversight of the British intelligence agencies, including the legal framework under which they operate, in response to the revelations emerging from files leaked by Edward Snowden.

The shadow home secretary, Yvette Cooper, is preparing to argue that the current arrangements are unsustainable for the government, and that it is damaging to trust in the agencies if ministers continue to hide their heads in the sand.

In a speech that represents Labour's most serious intervention since the controversy about the scale of state surveillance broke last summer, she will say: "The oversight and legal frameworks are now out of date. In particular that means we need major reforms to oversight and a thorough review of the legal framework to keep up with changing technology."

Nick Clegg, the deputy prime minister, by coincidence will also this week make a speech setting out his party's views on privacy and security.

Cooper will call for sweeping changes to strengthen the accountability of the intelligence agencies and a replacement to the out-of-date Regulation of Investigatory Powers Act 2000 (Ripa). Her speech eschews direct criticism of MI5, MI6 and GCHQ, and accepts that the leaks by the former National Security Agency contractor Snowden have damaged national security while highlighting legitimate concerns about privacy in the internet age.

She will also argue that ministers have responded to the revelations in a patronising way by trying to stifle debate on the online role of the police, intelligence and security agencies, or of the legal framework that governs their work. "The government can't keep burying its head in the sand and hoping these issues will go away," she will say in the speech to the thinktank Demos.

She will urge David Cameron to learn instead from President Obama, who has welcomed, and led, a debate in the US about the balance between security and liberty in the wake of the Snowden leaks.

British ministers, Cooper is expected to argue, "have provided neither reassurance nor reform. They have simply asserted that the British agencies are abiding by the law. They haven't explained what the law does, what the privacy safeguards are, whether the law is still up to date, or why the work the agencies do is important. Neither prime minister, deputy prime minister, home secretary nor foreign secretary have provided any leadership or response.

In contrast President Obama commissioned an independent review and set out areas for reform to protect US citizens' privacy and civil liberties, while also robustly defending the purpose and work of the security and intelligence agencies. "So in the US the debate is moving on. But here in Britain, it's barely started. That's not sustainable."

The speech is the product of extensive soundings with civil liberty groups, the spy agencies and the police, and makes the prospect of changes to the law on communications after the election highly likely. Cooper singles out the three intelligence commissioners as needing a "major overhaul", saying they operate as much in the shadow as the spies they oversee.

Her criticism is aimed at the secrecy of the work of three commissioners – Sir Anthony May, responsible for intercepts (covering the police and agencies), Sir Mark Waller, responsible for the intelligence services, and Sir Christopher Rose, responsible for surveillance by public bodies. She is expected to complain: "None of them have made substantial public statements in response to the Snowden leaks. They are responsible for checking whether the agencies are abiding by the law. Yet in the face of allegations that GCHQ was breaking the law they have been silent – neither saying they would investigate, nor providing reassurance."

Her speech concedes that Waller, the interception of communications commissioner, has said he will review the legal framework, but Cooper says: "Few know it is happening and there is no opportunity for the public to submit views." Waller has also been summoned to appear in front of the Home Affairs Select Committee later this month, after earlier declining to give evidence .

She will suggest Britain may need to consider an inspector general, along Australian lines, with the resources to provide wide-ranging and stronger oversight of all the agencies. She will argue that Britain lacks a fast and flexible system that can not only check current legal compliance but can regularly review the law.

Cooper will also argue the government needs to conduct a full review of Ripa, which governs interception regulation, including whether the new forms of communication have dissolved the once clear distinction between content and communications data – especially given the information agencies and private companies such as Facebook can gather on the pattern of visited websites.

Cooper's speech criticises the response to Snowden by the intelligence and security committee, a group of MPs appointed by the prime minister and currently chaired by former Tory foreign secretary Sir Malcolm Rifkind, arguing it simply has not had the capacity or resources for a full inquiry into the revelations. The committee's legitimacy would be strengthened, she adds, if it were always chaired by an MP from an opposition party, so it is not viewed as an extension of the government.