Brian Lord said the current situation was "unsustainable" as the Manchester terror attack cast a fresh light on the challenge intelligence services face in tackling extremism online and through encrypted messaging apps.
Mr Lord said: "I think when you have large organisations who provide ostensibly a public service to almost a quarter of the globe, I think those companies have to recognise that comes with a set of social responsibilities and not just an issue of profit."
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Britain should consider fining internet giants that fail to take down extremist content, says expert
Former GCHQ deputy director Brian Lord said the current situation was ‘unsustainable’
Common ground has to be found between the Government's demands and what is feasible for providers to do, adding: "I don't think the current position is sustainable."
Organisations who provide ostensibly a public service to almost a quarter of the globe, I think those companies have to recognise that comes with a set of social responsibilities and not just an issue of profit
Brian Lord – Former GCHQ deputy director
Ministers should consider a German-style system, where providers are fined millions of euros for failing to remove fake news from their sites, he said.
He told BBC Radio 4's Today programme: "I think we should consider it but as with all these issues, social media is here to stay and actually it's just as incumbent on the organisations themselves to adjust their approach to this as well as the threat of fines.
"I don't think it's either one or the other."
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Prime Minister Theresa May has put security at the heart of her election campaign
Former Lib Dem leader Nick Clegg
In the aftermath of the suicide bomb in Manchester, leaders of the G7 states, the US, UK, Canada, Japan, France, Germany and Italy, agreed a package of measures to step up the fight against terror.
Former Lib Dem leader Nick Clegg said he was sceptical about how encryption could be removed without “huge disruption” to daily life.
Speaking on Today, he said: “It has become part of the fabric of our data-driven modern economy and I think for ministers to keep saying, as they have done repeatedly, we are going to ban encryption, I just don’t see how you could do so without causing huge disruption to the rest of the way we now conduct our daily lives.
“But secondly a lot of these providers who provide this end-to-end encryption service are not even located in the United Kingdom so I am not sure how it would be possible for us.”
He said it was “odd” to ban the technology when ministers and Conservative MPs use encrypted messaging apps such as WhatsApp to communicate with each other.