Edward Snowden's disclosures of the scale of mass surveillance are "an embarrassing indictment" of the weak nature of the oversight and legal accountability of Britain's security and intelligence agencies, MPs have concluded.

A highly critical report by the Commons home affairs select committee published on Friday calls for a radical reform of the current system of oversight of MI5, MI6 and GCHQ, arguing that the current system is so ineffective it is undermining the credibility of the intelligence agencies and parliament itself.

The MPs say the current system was designed in a pre-internet age when a person's word was accepted without question. "It is designed to scrutinise the work of George Smiley, not the 21st-century reality of the security and intelligence services," said committee chairman, Keith Vaz. "The agencies are at the cutting edge of sophistication and are owed an equally refined system of democratic scrutiny. It is an embarrassing indictment of our system that some in the media felt compelled to publish leaked information to ensure that matters were heard in parliament."

The cross-party report is the first British parliamentary acknowledgement that Snowden's disclosures of the mass harvesting of personal phone and internet data need to lead to serious improvements in the oversight and accountability of the security services.

The MPs call for radical reform of the system of oversight including the election of the membership of the intelligence and security committee, including its chairman, and an end to their exclusive oversight role. Its chairman should also be a member of the largest opposition party, the MPs say, in direct criticism of its current head, Sir Malcolm Rifkind, who is a former Conservative foreign secretary.

Rifkind, however, said he had read the report, and had concluded: "The recommendations regarding the ISC are old hat. For several years, Mr Vaz has been trying to expand the powers of his committee so that they can take evidence from MI5, MI6 and GCHQ. This is what this bit of his report is all about."

Rifkind attempted to head off some of the MPs' conclusions by announcing that the ISC would conduct its own inquiry into personal privacy and state surveillance. He also attacked Snowden and his supporters for their "insidious use of language such as mass surveillance and Orwellian" – which, he argued, "blurs, unforgivably, the distinction between a system that uses the state to protect the people, and one that uses the state to protect itself against the people".

However, a complete overhaul of the "part-time" and under-resourced system of oversight commissioners is recommended by the MPs, as is an end to some of the secrecy surrounding the Investigatory Powers Tribunal – the only body that is able to investigate individual complaints against the security agencies.

A parliamentary inquiry into the principal legal framework that legitimises state communications surveillance, the Regulation of Investigatory Powers Act 2000, should be launched, they say, to bring it up to date with modern technology and improve its oversight safeguards.

The committee also voices strong concerns that a data protection ruling by the European court of justice last month has left the legality of the bulk collection of communications data by the phone and internet companies in serious doubt. "It is essential that the legal position be resolved clearly and promptly," say the MPs, who reveal that the home secretary, Theresa May, has ordered urgent work into the ruling's full implications for the police and security services.

The MPs say they decided to look at the oversight of the intelligence agencies following the theft of a number of National Security Agency documents by Snowden in order to publicise the mass surveillance programmes run by a number of national intelligence agencies.

Their report says Alan Rusbridger, editor of the Guardian, responded to criticism of newspapers that decided to publish Snowden's disclosures, including the head of MI6's claim that it was "a gift to terrorists", by saying that the alternative would be that the next Snowden would just "dump the stuff on the internet".

The MPs say: "One of the reasons that Edward Snowden has cited for releasing the documents is that he believes the oversight of security and intelligence agencies is not effective. It is important to note that when we asked British civil servants – the national security adviser and the head of MI5 – to give evidence to us they refused. In contrast, Mr Rusbridger came before us and provided open and transparent evidence."

The report makes clear the intelligence chiefs should drop their boycott of wider parliamentary scrutiny. "Engagement with elected representatives is not, in itself, a danger to national security and to continue to insist so is hyperbole," it says.

But a move by Labour and Lib Dem MPs to congratulate the Guardian and other media outlets for "responsibly reporting" the disclosures – saying they had opened a "wide and international public debate" – was voted down by four Tory MPs.

Yvette Cooper, the shadow home secretary, said the report showed there was a cross-party consensus behind Labour's proposals, including reform of the commissioners system and an opposition chair of the ISC. "The government should now set out plans for oversight reforms," she said.

Nick Clegg has also outlined proposals for reforming the oversight system.

Cooper added that the select committee had added their voice to the growing number of MPs, who were calling for reform. She said that the police and security services needed to keep up with the challenges of the digital age but stronger safeguards and limits to protect personal privacy and sustain confidence in their vital were also needed: "The oversight and legal frameworks are now out of date," said the shadow home secretary.Emma Carr, of Big Brother Watch, the privacy campaign group, said: "When a senior committee of parliament says that the current oversight of our intelligence agencies is not fit for purpose, ineffective and undermines the credibility of parliament, the government cannot and must not continue to bury its head in the sand."

Last night, a statement by the Association of Chief Police Officers (Acpo) and the Terrorism and Allied Matters (TAM) Board – consisting of assistant commissioner Cressida Dick, chief constable Sara Thornton, chief constable Sir Peter Fahy, chief constable Chris Sims, chief constable Mark Gilmore and chief constable Matt Baggott – said they were "concerned" the committee had recommended that responsibility for counter-terrorism policing should be moved to the National Crime Agency.

The statement described it as "a decision that does not appear to supported by the evidence and is based on an apparent misunderstanding of the role played by the Metropolitan Police Service."Counter-terrorism policing is not directed through a single lead force but rather has responsibility vested in nine chief constables across the UK in areas where the threat is considered to be the greatest. These chief constables act collaboratively and effectively on behalf of all forces, while at the same time maintaining close and critical links into local policing."

The statement added: "The Home Secretary has previously confirmed that she will conduct a review of counter-terrorism structures. We welcome any such review and look forward to participating fully and constructively in it. "

The Home Office said: "Our security agencies and law enforcement agencies operate within a strict legal and policy framework and under the tightest of controls and oversight mechanisms. This represents one of the strongest systems of checks and balances and democratic accountability for secret intelligence anywhere in the world."