The five biggest internet companies in the world, including Google and Facebook, have privately delivered a thinly veiled warning to the home secretary, Theresa May, that they will not voluntarily co-operate with the "snooper's charter".

In a leaked letter to the home secretary that is also signed by Twitter, Microsoft and Yahoo!, the web's "big five" say that May's rewritten proposals to track everybody's email, internet and social media use remain "expensive to implement and highly contentious".

The private letter, which has been passed to the Guardian, is part of a series of continuing confidential discussions between the industry and the Home Office. It says that May's "core premise" to create a new retention order requiring overseas internet companies to store the personal data of all their British-based users for up to 12 months has "potentially seriously harmful consequences".

The leading US-based internet players have also told the home secretary that her proposed £1.8bn communications data plan puts at risk Britain's position as a leading digital nation and jeopardises the UK's leading role in promoting freedom of expression on the internet around the world.

The collaboration of the internet giants is vital for the success of May's communications data project but they warn that it opens the door to a "chaotic world" in which every country seeks to impose conflicting demands on companies in sensitive areas such as the collection and storage of personal data.

They say it would threaten the open nature of the internet – which means that it is available to anyone who accesses it – and would undermine their ability to offer a global service by companies working within the legal framework of their home jurisdiction.

The private letter is dated 18 April when the coalition's battle over whether the legislation should be in this year's Queen's speech was at its peak. Nick Clegg blocked the bill days later but both May and the defence secretary, Philip Hammond, have demanded that it be revived in the wake of the Woolwich terrorist murder.

The companies say that while they are prepared to make "reasonable accommodations" to reflect local concerns and legal requirements, what May is proposing is very different.

"We do not want there to be any doubt about the strength of our concerns in respect of the idea that the UK government would seek to impose an order on a company in respect of services which are offered by service providers outside the UK," it says.

"The internet is still a relatively young technology. It brings enormous benefits to citizens everywhere and is a great force for economic and social development. The UK has rightly positioned itself as a leading digital nation.

"There are risks in legislating too early in this fast-moving area that can be as significant as the risks of legislating too late."

The internet industry's letter was sent to May after they had been confidentially briefed by Home Office ministers and officials on her revised proposals to meet objections from a joint parliamentary scrutiny committee that the measure "trampled on the privacy of British citizens".

The companies also detail an alternative approach to extend existing arrangements for them to meet the requests for personal data from the police and security services, including a new UK-US bilateral initiative to make the process faster and more efficient.

They argue that this would be more effective and reduce the need for new primary legislation that would be both expensive to implement and highly contentious.

Home Office ministers have always said they hoped to rely on voluntary collaboration with the main internet companies, such as Facebook and Google, on handing over sensitive personal data about British users to make the "snooper's charter" work.

They have so far declined to spell out how they would force them to hand over data but officials have confirmed that, in extreme circumstances, they would consider using probes, also known as "black boxes", to intercept such data from overseas-based services as it passed through British communications networks.

Clegg said on his weekly LBC local radio phone-in on Thursday that his decision to block the bill on the basis that it was "unworkable and disproportionate" was partly based on evidence from "the Facebooks and the Googles" that important parts of what was being proposed wasn't workable.

"The industry … upon whose co-operation we rely on to go after the bad people, just said it wasn't workable in its present form," the deputy prime minister said.

"They said no other country in the world has done this, no other democracy in the world has done this. It would set a sort of dangerous precedent and might then be followed by much less liberal and law-abiding regimes."

The home secretary said at the weekend that access to communications data was essential for the law enforcement and intelligence agencies to do their job and they must be given the "tools they need" to fight crime, including paedophiles and terrorists.

A Home Office statement issued earlier this week said: "The government is continuing to look at ways of addressing this issue with communication service providers. This may involve legislation."