Four former home secretaries have urged Nick Clegg to drop his opposition to the so-called snooper's charter, warning that "coalition niceties must not get in the way of giving our security services the capabilities they need to stay one step ahead of those that seek to destroy our society".

In a letter published in the Times, the politicians – Labour's Jack Straw, David Blunkett and Alan Johnson, and the Conservative Lord Baker – argue that the new internet monitoring powers contained in the communications data bill are a vital tool in the fight against terrorism.

On Thursday, the deputy prime minister reaffirmed his objection to the bill, which he blocked from the Queen's speech. He is opposed to plans to allow the security services access to up to a year's worth of records of online communications and internet browsing – though they would only be able to see the content of messages with ministerial approval.

"I think a much wider-ranging snoopers' charter in which all the websites you visit … would be recorded and we would be able to keep an eye on the traffic that comes from internet service providers in other parts of the world – I think those two things, which are the other bits that were proposed in the so-called snooper's charter, have proved to be either disproportionate in my view or not workable," he said on his LBC 97.3 radio phone-in.

But he was accused of putting internet firms' interests above national security as critics – spurred by the killing of soldier Lee Rigby in Woolwich – continued to call for the legislation to be revived.

The Times letter was also signed by Lord King, a Tory former defence secretary, and the Liberal Democrat Lord Carlile, the former independent reviewer of UK anti-terror laws.

"We find it odd that many critics of the bill prefer to champion the rights of corporations over democratically accountable law enforcement agencies," they wrote. "When such a threat reveals itself, government has a duty to ensure they can do all they can to counter it.

"Far from being a 'snooper's charter', as critics allege, the draft bill, seeks to match our crime-fighting capabilities to the advances in technologies. The proposed communications data bill does not want access to the content of our communications but does want to ensure that enough data is available in the aftermath of an attack to help investigators establish 'who, where and when' were involved in planning or supporting it."

Straw said that if safeguards demanded by a cross-party committee were included in the legislation, there was "no particular reason" it could not be passed in the Commons with Labour support.

In a swipe at Clegg, he told BBC2's Newsnight: "He needs to think about what is more important: supporting Google and Amazon and these other American behemoths; or supporting security and reassurance for the British people."

Civil liberties advocates criticised the letter's signatories. Emma Carr, deputy director of Big Brother Watch, said: "Several of the signatories to this letter argued that ID cards, 90-day detention without trial and a million innocent people on the DNA database were all necessary to keep us safe. Fortunately the government did not succumb to their scaremongering on those issues, and nor should it on the question of whether in modern Britain we want the state to be undertaking blanket monitoring of our emails, web browsing and social media messages."