Amber Rudd’s call for “no hiding place for terrorists” on the web echoes and revives David Cameron’s 2015 proposal to ban end-to-end encryption on services such as WhatsApp.

That proposal was dropped from the “snooper’s charter” legislation because of widespread opposition in the tech industry and from Conservative libertarians, including David Davis, now Brexit secretary and one of the home secretary’s cabinet colleagues.

Tim Cook, the chief executive of Apple, raised concerns at the time of Cameron’s proposal to place a legal obligation on internet companies to help in operations to bypass the encryption of their services. “Any backdoor is a backdoor for everyone. Everybody wants to crack down on terrorists. Everybody wants to be secure. The question is how. Opening a backdoor can have very dire consequences,” he said.

Rudd said on Sunday that she wanted people like Cook to think again about helping to build “backdoors” into services so that end-to-end encryption would be banned. Encryption is unbreakable code that currently ensures that online messages and transactions on services such as WhatsApp are unreadable if they are intercepted by any third party, including the security services.

Davis spelled out what those dire consequences might be at the time the issue was last debated. He said in a Financial Times article in November 2015: “Such a move would have had devastating consequences for all financial transactions and online commerce, not to mention the security of all personal data. Its consequences for the City do not bear thinking about.”

Davis added that provisions in the Investigatory Powers Act, then being brought before parliament as a bill, would prevent new encrypted services from being offered in Britain. “Instead, government policy is likely to strangle UK tech businesses, by prohibiting the spread of encryption to those services that do not already use it,” his FT article continued. “This will put our communications companies at a severe disadvantage, as their overseas competitors are permitted to offer fully secure services forbidden to UK companies.”

It is likely that Rudd’s revived proposal will face the same scale of criticism and the warning that it could severely handicap Britain’s growing digital industry at a time of great uncertainty in a post-Brexit world.

The home secretary’s demand for wider powers to ban encrypted services is surprising in the aftermath of the Westminster terror attack, even after the disclosure that Khalid Masood used the encrypted WhatsApp service just before he launched his deadly attack.

This is because on Friday, even a former head of GCHQ had acknowledged that the Investigatory Powers Act – the snooper’s charter legislation, which has only just reached the statute book – already contained the most sweeping digital surveillance powers in the western world.

The home secretary is due meet the web giants Google, Facebook and Twitter on Thursday and demand that they do more to deny terrorist groups the use of their social media platforms and access to related advertising revenue. The meeting is likely to be a replay of a summit held at the Cabinet Office on Friday a week ago, when junior Home Office and Cabinet Office ministers read the web companies the Riot Act.

MPs such as Yvette Cooper, the chairman of the Commons home affairs committee, have rightly criticised the web companies for failing to remove offensive videos from YouTube and demanded that they carry out far more proactive searches for terrorist and extremist material that can be used to radicalise vulnerable individuals.

But as the companies point out, part of the problem lies in the lack of any legally robust definition of what constitutes extremist material. Whitehall lawyers have been working for the past 18 months on a definition that can be used to curb non-violent extremism without being struck down by legal challenges based on freedom of expression. The lawyers have failed to settle on one, and the web companies say that while they can act swiftly to take down illegal material, it is much more fraught if the material is regarded as offensive but not actually banned.

The web companies also point out that some of the Islamist or jihadi videos complained about do not actually infringe their guidelines. This is because they consist of Islamist songs or general material about jihad and not the kind of specific incitement that falls within the legal definition. It is akin to having demanded a ban on Irish Republican songs at the height of the Troubles.

In the face of these problems, the threat by the home secretary of new laws to force the web companies to act may prove problematic.