Isis and other terrorist groups are winning an ongoing "netwar" against authorities trying to stop the spread of extremist material online, a new report has warned.
Research by the Policy Exchange think-tank found that almost three quarters of the public want large internet companies to do more to find and delete content that could radicalise people.
Another 65 per cent people thought firms were not doing enough to combat the phenomenon and while respondents were split over whether internet companies or the Government should take ultimate responsibility, 75 per cent supported the introduction of an independent regulator.
Three quarters of the 2,000 people surveyed wanted new laws to criminalise the persistent viewing of extremist material online, and 73 per cent thought the possession of propaganda should be illegal.
The Policy Exchange warned that such powers would need to be constrained to avoid "undue infringement of civil liberties", but called for a new approach to combat the terror threat.
Its analysis found that jihadi content was accessed more frequently in the UK than anywhere else in Europe, with the country in fifth place globally behind Turkey, the US, Saudi Arabia and Iraq.
General David Petraeus, the former director of the CIA, said current situation was "clearly unacceptable".
The retired general, who commanded Nato forces in Afghanistan, said the attempted bombing in Parsons Green underscored the threat generated by instructions and other materials available online.
"The fight against Isis, al-Qaeda, and the other elements of the global jihadist movement has become the defining struggle of the early 21st Century," General Petraeus said in a foreword to the report.
"That struggle has increasingly been contested not just on the ground, but in a new domain of warfare, cyberspace."
He cautioned that while few doubt Isis' physical "caliphate" in Syria and Iraq will be eradicated along with most of its militants, the group will continue to inspire atrocities around the world by targeting the most vulnerable sections of society with its "poisonous ideology".
General Petraeus added: "The events of the last decade-and-a-half attest to the durability and adaptability of the jihadist movement.
"I have seen how the defeat of jihadist forces in one theatre does not equate to victory in the overall struggle - or, sadly, even to enduring success in that theatre."
General Petraeus said that like its predecessor al-Qaeda, Isis will continue to operate either as an insurgency, terrorist movement or ideological project that continues seeking to radicalise followers and inspire terror attacks around the world.
"It is clear that that our counter-extremism efforts and other initiatives to combat extremism on line have, until now, been inadequate," he added.
"I do not think we have yet developed all the 'big ideas' needed to come to grips with the problem, much less the policies and methods to combat it."
The Policy Exchange report found that while Isis propaganda has declined on Twitter, Facebook and other mainstream platforms amid increasing cooperation with those companies, it continues to flourish elsewhere.
The terrorist group has been able to maintain a consistent virtual output of thousands of videos, radio bulletins, magazines and less formal messaging through encrypted apps like Telegram and its own network of websites.
To combat intensifying efforts to remove its content in the three years since the Islamic State was declared, Isis has developed tools like an automated email service, apps and Firefox plug-ins to ensure followers can access its key propaganda outlets.
While direct access has become more difficult, researchers and journalists are unwittingly making extremist material more "findable" by reporting on Isis' tactics, the Policy Exchange warned.
Dr Martyn Frampton, the lead author of the report, said authorities were playing a fruitless game of "whack-a-mole" reducing individual pieces of content and needed to go further to disrupt dissemination networks.
"The evidence suggests that we are not winning the war against online extremism and we need to consider options for change," he added.
"If the internet companies won't do what their customers want and take more responsibility for removing this content, then government must take action through additional regulation and legislation."
In May 2016, Facebook, Microsoft, Twitter and YouTube signed up to an EU-sponsored code of conduct that pledged to establish improved ways to take down illegal hate speech and other extremist material.
But Isis' "swarmcast" - an interconnected network that constantly reconfigures itself to resist disruption - has allowed it to continue distributing its propaganda on file sharing services, encrypted apps, websites and social media.
The Policy Exchange called for the Government's proposed Commission for Countering Extremism to be empowered to oversee the removal of extremist content, and for the possible creation for an independent online regulator that could financially penalise companies that fail to remove extremist content.
But analysts have warned that the role of the internet in radicalisation has been overplayed, with research showing that personal relationships and real-world networks play a defining role.
A recent UN report showed that Isis' foreign fighters are likely to be young, disadvantaged economically and educationally, and from a marginalised background - all factors requiring Government intervention beyond counter-extremism.
The same research report found that among surveyed fighters, the internet played "a far less significant role as an independent source of radicalisation than is generally assumed, and certainly a far less significant role than real life contact".
Authors found that would-be jihadis went online to confirm and strengthen ideas that were already taking root, adding: "The internet then played a key role in reinforcing a decision that had in part been taken already."
Major-General Chip Chapman, the former head of counter-terrorism in the Ministry of Defence, said the internet made a "convenient" target for the Government.
"They are picking on an unspecific part of what the total problem is and it's not addressing the core issues," he told The Independent.
"Radicalisation is not just an online process, it's offline as well because it's really to do with friendships and networks.
"The internet is really just a place of congregation like schools, universities and prisons."
Major-General Chapman said cohesion and integration were historical contributors to radicalisation that remain unaddressed.
"The core problem is that 70 per cent of people who have been arrested for terrorism in the year to June are either British or dual nationals," he added.
"That's the real elephant in the room that they're not really looking at by picking on the internet."
He cautioned that social media was worsening confirmation bias and making it more difficult for young people to gain the "intellectual resilience" needed to question propaganda.
The debate comes amid warnings by the security officials that the threat of Isis-inspired terror attacks is increasing as it becomes more difficult for jihadis to travel to its waning territories.
Around 3,000 extremists are being monitored as potential threats, with a wider pool of 23,000 people who have previously come onto the radar of intelligence agencies and police.
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