Occasionally in the long history of British policymaking someone manages to break through the confusion and reset the terms of an apparently unresolvable public argument. Edwin Chadwick on the poor law and public health, William Beveridge on the welfare system and Leslie Scarman on the police all changed things for generations – and for the public good – in their respective fields. The question today is whether the name of David Anderson – Britain’s watchdog on terrorism laws – should be added to the list of these national reformer-reconcilers.

With a fair wind behind it, his report on the future of surveillance laws, published yesterday, may eventually prove to have poured calming oils on a stormy argument that British governments have often seemed incapable of resolving. If Anderson’s plea is taken seriously, and we wipe the slate clean and start again on Britain’s efforts to balance security and privacy in the pursuit of crime in the borderless online world, his report really could be the turning point that policymakers have looked for and missed ever since 9/11.

After so many failures, only the naive will confidently predict success. When a state is interested in citizens’ private conversations – whether their letters in the 19th century, phone calls in the 20th or emails and social media contacts in the 21st – we are inevitably in a place where individual liberty is being tempered and abuses may occur. But there is no doubting the accuracy of Anderson’s critique of the current morass of powers and uncertainties that make up the state’s attempts to intercept and disarm the public’s enemies without conferring sweeping general powers on state agencies: “Fragmented, obscure, under constant challenge and variable in the protections it affords the innocent,” as Anderson puts it in his report.

In place of this Anderson offers something important for both sides of the entrenched argument between privacy and security in the ever-changing online world. To the state he offers a comprehensive new law, the maintenance of the compulsory data retention powers that critics describe as mass surveillance – exaggeratedly, in my view – as well as a conditional but highly controversial right to access the online browsing habits of suspects. To the individual citizen Anderson offers a case-by-case system of judicial oversight of executive surveillance operations – taking ultimate authorisation out of the hands of ministers – along with a strengthened independent regulatory system. There is nothing wrong in principle with this approach. It cannot be a zero-sum game.

The big unknown, which needs to be carefully and honestly debated in the weeks before the government comes forward with legislation based on Anderson, is whether this is a fair balance and can be trusted in practice. There is a danger that the general welcome for Anderson will encourage MPs not to scrutinise the detail. Where deadly terrorist dangers are involved, much of the public tends to trust the government to do the right thing, anyway and be impatient with concerns about the civil liberties of suspects. Relying on this, governments are often emboldened to dismiss libertarian concerns. History is littered with examples of people who have allowed themselves to swallow one assurance too many.

Whether Anderson succeeds where so many have failed since 9/11 will depend on two things, one general and one particular. The general one is whether he can win public confidence for the trade-offs and the approach he proposes. Anderson is never going to persuade the most secretive securocrats to test their suspicions in front of a judge. But he is never going to persuade the out-and-out online libertarians that intrusive powers will be used virtuously. The two sides are united only in mutual certainty that the other offers dystopia. But as the report rightly says, the “silent majority sits between those poles, in a state of some confusion”. The few who read and study Anderson may be persuaded about his approach. But what about the overwhelming majority who will never go near it?

This is where the particular issue comes in. The viability of Anderson’s new approach depends in large measure on whether Theresa May is brave enough to be the great home secretary she occasionally seems capable of being. She will not lack for political allies, judging by the responses to the report. Labour, liberal Tories and Scottish nationalists seemed willing to give her the chance to make Anderson’s balanced package work. The lawyers and civil liberty groups offered a cautious amber light too. The great unknowns are the securocrats and May herself.

The post-Snowden debate in this country has seemed like a full-pelt dialogue of the stone deaf

The argument between privacy and security is venerable indeed. It would be a stretch to say it goes right back to Magna Carta, whose 800th anniversary falls on Monday. But it certainly goes back as far as the illegal searches blocked in the Entick v Carrington case in the 1760s, and a digital version of that dispute has been at boiling point since the resurgence of terrorism and the Edward Snowden revelations about state data collection.

At times, though, the post-Snowden debate in this country has seemed like a full-pelt dialogue of the stone deaf. The champions of online privacy have often been unwilling to concede, sometimes even as a matter of principle, the claims of the guardians of the state for necessary powers of intrusion to protect the public. But the security world has been every bit as obdurate in the opposite way, indeed more so – insisting that the dangers of further terrorist attacks always trump every privacy concern, and dismissing Snowden as a dangerous criminal.

If anything, the Conservative-Liberal Democrat coalition government preserved in aspic some of that stand-off between security and privacy. The deeper instincts of each party – for good order in the Tory case, for individual liberty in the Lib Dem one – seemed to be intensified by the coalition, not to generate a synthesis that both could own together. Paradoxically, a majority Tory government may now offer a better chance of giving permanence to Anderson’s balanced recasting of this hugely complex and difficult subject.