But The Laws We Already Have Worked?

...the proof being that the perpetrator is in jail for life:

A new offence to cover lone individuals planning non-terrorist mass killings should be considered in the wake of the Southport attacks, the UK's terror watchdog has said. However the independent reviewer of terrorism legislation, Jonathan Hall KC, says the definition of terrorism should not be expanded or changed.

Why does it need to be? Surely it simply needs to be applied, as it wasn't in this case.  

Mr Hall considered whether the definition of terrorism itself should be changed to include mass violence without a political, religious, racial or other ideological motivation, but concluded it should not. "Redefinition would alter the landscape. It would risk major false positives – the prosecution of people who by no stretch of the imagination are terrorists – and extend terrorism liability into novel terrain," Mr Hall said.

"People swapping violent war footage would be at risk of encouraging terrorism, resulting in unacceptable restrictions on freedom of expression."

And we all know why he stopped short - not so acedemics could have online discussions about violence without the fear of plod breathing down their necks, but so the idiots that support Hamas and other Islamic terror organisations can spread their propaganda unaffected. 

However, Mr Hall said there was a clear risk to the public of people who are interested in carrying out acts of mass violence, including school massacres. Currently there is no law against preparing for such an attack which "means that no prosecution would be available if the police raided an address and found careful handwritten but uncommunicated plans for carrying out a massacre". As a result, he is recommending the government considers creating a new offence, similar to the offence of preparing an act of terrorism.

The lack of such a law didn't seem to hinder this arrest.  

As part of his report Jonathan Hall KC considered what should happen with young people like Axel Rudakubana, who are referred to the counter-terrorism Prevent programme, but are not taken on because they do not have a clear ideology. "If they are not to be managed by counter-terrorism police, who will 'own' the risk?", he asked.

We will. We always do.