The British government must follow Barack Obama's lead and introduce sweeping reforms to government spy agencies after revelations of mass surveillance by whistleblower Edward Snowden, an influential Conservative backbench MP said on Sunday.

Dominic Raab, who with Liberal Democrat Julian Huppert and Labour's Tom Watson secured a discussion on oversight of intelligence and security services in October, said Britain's response so far to the revelations that the US and UK spy agencies were monitoring vast amounts of personal data was "comatose".

He urged the government to follow the lead of the US president who on Friday announced the scrapping of databases holding a record of every call made in the US after acknowledging there was a "potential for abuse".

On Sunday Labour MP Hazel Blears, who sits on parliament's intelligence and security committee, admitted its members knew about an NSA program codenamed Dishfire, which it was revealed last week collected up to 200m text messages a day from around the globe.

Asked on the BBC's Sunday Politics show if the committee knew GCHQ had the capability to use the program or to get Dishfire material from the NSA, she replied: "I knew and my committee knew that we had the capability to collect metadata.

"These days people don't write letters, they don't use landline telephones, they use Skype, email, internet texting, and therefore it's important that the agencies are able to keep up with that technological change within a proper legal framework."

Writing in the Sunday Times, Raab argued that the revelations about the operating methods of the NSA and GCHQ, including Dishfire, had "shattered old assumptions about the relationship between the citizen and the state".

He added: "Reaction in America has brought sweeping reforms. It's high time we in Britain put our own house in order."

Raab praised Obama's decision to roll back the US government database, introduce the need for judicial approval of data gathering (except in emergencies), curtail the breadth of surveillance and introduce greater transparency over requests to banks, phone companies and internet providers for personal records.

"By comparison, the British reaction to this full-frontal assault on our privacy seems comatose," he said.

"The government-appointed intelligence and security committee is looking into the previous Snowden disclosures, but has too often been given the runaround by the spooks.

"We need a swift, judge-led inquiry with full powers of disclosure to determine the real scale of UK surveillance and its legality, and offer parliament recommendations to clarify the scope of legitimate surveillance and strengthen safeguards to prevent abuse.

"That is the only way to safeguard our privacy as citizens and restore some integrity to the vital work of the intelligence agencies."

The coalition's attempt to address the issue – with a proposed communications data bill in 2012, which was designed in part to put existing surveillance methods on a firmer legal footing – had failed because the "sheer scale of surveillance envisaged" had sparked a backlash, he wrote.

The British government risked facing a battle with phone and internet companies "that pride themselves on protecting their customers' data", while also leaving themselves vulnerable "to challenge in the courts, potentially exposing the taxpayer to enormous costs", he warned.

Raab argued that claims that intrusion into the public's private lives had thwarted terrorist plots did not stand up.

"In a debate last October, I asked Sir Hugh Orde, president of the Association of Chief Police Officers, whether he could name or recall any case where such communications data had been decisive in saving life or limb. He couldn't," wrote the backbencher.

This week the Guardian's editor-in-chief Alan Rusbridger accused Britain's political class of ignoring the significance of Snowden's revelations in the hope they would go away rather than address key issues over mass surveillance that have provoked such heated debate in America.

"I think there is a degree of complacency here. There has been barely a whisper from Westminster. I think they are closing their eyes and hoping that it goes away," he said.

"But it won't go away because it's impossible to reform the NSA without having a deep knock-on effect on what our own intelligence services do."

Blears said that the intelligence and security committee was committed to ensuring the issue did "not go away" and had launched an inquiry into is the current legal framework.

"We've had massive technological change, we need to look at that … We obviously have to be mindful that some of the information could well be classified, but I think on the committee there is a genuine real commitment here to say look, there's a big debate going on, let's see if our system actually is as robust as we can make it."