Police have already made several arrests following the horrific violence in Southport earlier this week when several children were stabbed to death at a Taylor Swift Christmas party. Police are continuing to hunt the other perpetrators – but the more difficult question is how to deal with the rise of the far right, whose brutal followers are behind the unrest and the spread of disinformation and fake news that fuels this extremism.

Home Secretary Yvette Cooper has said she will examine calls to add the English Defence League to the list of proscribed terrorist organisations alongside other far-right groups such as National Action.

Few would miss them except their narrow-minded supporters, especially after their recent violence in London, which was largely in response to the pro-Gaza protests. It would no doubt be a relief for the police not to be subjected to renewed violence and to have a new weapon to target the group’s leaders.

The sight of another brutal protest in Whitehall last night, which resulted in over 100 arrests, may have reinforced the feeling that – in the words of the protesters themselves – enough is enough.

However, the legal definition of terrorism is narrow and it is therefore uncertain whether the EDL, however abhorrent it may be, meets the necessary conditions for a ban.

Previous Home Secretaries have decided against it on the advice of their lawyers. And it is not obvious that inciting thugs to carry out a misguided shooting spree in Southport will change anything. Even breaking up the EDL alone would not get to the root of the problem. The bigger challenge is that conspiracy theories and outright lies on the internet are increasingly poisoning public debate and encouraging the rise of extremism and violence.

In the Southport case, the violence appears to have been fuelled by a false but widely circulated online claim that the 17-year-old suspect, born in Cardiff to Rwandan parents, was a Muslim asylum seeker who arrived in the UK on a small boat last year.

The organization Tech Against Terrorism has identified a Russian news channel as one of the proponents of this claim, raising suspicions that this week’s violence was at least partly instigated by the Kremlin as an act of hostile state aggression.

In theory, this would bring the new National Security Act and the Online Safety Act, or both, into play, as both contain provisions to curb the spread of disinformation.

But Jonathan Hall KC, the government’s terror watchdog who was also recently given the task of reviewing state threat legislation, warned in a speech two weeks ago that he was “sceptical” that the new powers to combat foreign interference could be a “safeguard”. He suggested instead that “laws requiring much more transparency from platforms” were needed to ensure they were doing enough to prevent such activity on their sites.

That shows the government still has a lot of work to do when it comes to disinformation resulting from foreign influence. The same is true of other aspects of the threat. One example is the provision in last year’s Online Safety Act that makes it a criminal offence to spread false information that could cause “significant psychological or physical harm” – as was indisputably the case with Tuesday’s violence. So too are the duties the law imposes on social media giants. The Home Secretary spoke yesterday of companies needing to take “some degree of responsibility” for the content on their sites, rather than resorting to legal threats. If that responsibility is not shown and the flood of inflammatory disinformation continues, pressure will mount for a more forceful response.

The law cannot stop people from carelessly indulging in conspiracy theories, as Nigel Farage did when he disingenuously questioned whether the police, who ruled out a terrorist link between both crimes, were deliberately withholding information about the Southport attack and the stabbing of a soldier in Kent. More accountability is needed, particularly from elected politicians, to avoid drifting into a Trump-esque world of alternative “facts”. Schools must also redouble their efforts to teach young people to rely on trustworthy sources.

There is also the threat of renewed debate about how to deal with propagandists such as Tommy Robinson, the founder of the EDL and largely responsible for the worrying rise of the far right that has plagued our country in recent years.

The government commission to combat extremism has recommended the introduction of a new criminal offence called “hateful extremism” to catch hate preachers – both Islamists and right-wing extremists.

Skeptics warn that it is difficult to find a sufficiently precise definition that is legally viable without compromising freedom of expression.

While there are no easy answers, Ms Cooper and Prime Minister Sir Keir Starmer are aware that calls for more action are likely to grow.

Martin Bentham is home affairs editor of the Evening Standard.