Just after 2:30pm yesterday afternoon, a terrorist mowed down pedestrians with a car on Westminster Bridge before jumping out near Parliament and stabbing a police officer to death. Three people were murdered, forty were injured, and the attacker was shot dead. The Islamic State (Isis) has now claimed the attack.

The most important question is whether the terrorist had co-conspirators. Prime Minister Theresa May told Parliament this morning that it is "believed that this attacker acted alone". It is crucial that this is not misread as saying that the attacker was a 'lone wolf'.

The arrests in Birmingham overnight suggest that this killer could have been part of a broader network, which would be consistent with the pattern of IS behaviour.

In a new report for the Henry Jackson Society, documents 152 foreign Isis attacks in 34 countries since 2002, the vast majority in the past two years. In nearly three-quarters of the cases the attacks have a direct link to the organisation, and those without often have accomplices who assist in the atrocities in some way.

Just 15% of the attacks have been by inspired individuals, who had no demonstrated connection to Isis or anyone else in planning or executing their attack.

In September 2014, Isis's official spokesman, Taha Falaha (Abu Muhammad al-Adnani), issued an infamous call for Muslims around the world to cast "fear into the hearts of the cross worshippers", meaning westerners, by killing them with any means available – guns, knives, rocks, cars, or poison. At a minimum "spit in his face", Falaha said, and if you find yourself unable to do so "then review your religion".

Westminster attack
23 March 2017: A police officer lays flowers on Whitehall around a photograph of police officer Keith Palmer who was killed in the Westminster attacks Justin Tallis/AFP

In the months leading up to Falaha's speech, Isis had already begun constructing its European network, but the speech would incite a wave of attacks from Canada and America to Australia to France. In 2015, the Isis networks matured and the attacks came more clearly under Isis control. In France, a series of mini-plots directed by Isis distracted security services as the November 2015 mass atrocities in Paris were prepared.

In what turned out to be his last speech in May 2016, Falaha asked that Muslims make Ramadan "a month of suffering for the kuffar (unbelievers) everywhere". From the onset of Ramadan on 6 June until the end of 2016 there were 58 attacks in 26 separate states killing more than 1,000 people – fully half of the total number of people killed by Isis in external attacks since 2002. In the whole of 2015 there had been 50 attacks killing about 900 people.

Clearly Isis's foreign terrorist attacks are becoming more frequent and more deadly. From the summer of 2016, Isis has developed a model of claiming attacks that involves operatives sending a video pledging allegiance to its caliph before the attack and receiving instructions for the commission of an attack from IS's foreign intelligence service, Amn al-Kharji. These videos are then released after the atrocities by IS's Amaq 'News' Agency. Given that the terrorist incidents usually end with the Isis operative being killed, the videos are proof in themselves than Isis had input on the attack and approved it before it was committed.

The guides from Amn al-Kharji had been active in 2015, notably the British hacker Junaid Hussain and some other English-speaking operatives. Their reach expanded in 2016, with IS appearing to set up area managers based on language, French and Turkish primarily, but Amn al-Kharji has directors for Indonesia, Malaysia, and even India.

Britain has experienced eight attacks or attempted attacks by the Isis movement. Anomalously, most of the attacks have not had a direct connection to Isis. The exception was the plot rolled up in July 2015 by Junead Khan and Shazib Khan in Luton as they planned to attack an American military installation under Hussain's guidance.

As the core has shrunk, Isis's foreign reach has expanded.

The most recent attempted Isis attack was intended to be a Paris-style massacre in west London, which was thwarted in September. There have been three "successful" attacks in Britain. The first was in 2007, when Bilal Abdullah and Kafeel Ahmed drove a car loaded with explosives into Glasgow Airport. Isis claimed it a year later. In December 2015, Muhiddin Mire attacked travellers on the tube with a knife and in February 2016 a network in Rochdale assassinated an imam, Jalal Uddin, whom they accused of black magic.

What to make of all this? At least two important practical implications obtrude from these findings.

First is the notion that, as Brett McGurk the US representative to the anti-Isis Global Coalition put it, the "common denominator ... driving ... young people to this movement ... is this notion of a historic caliphate" and therefore "we have to shrink the core". As the core has shrunk, Isis's foreign reach has expanded.

Part of this is the Coalition's own doing. By focusing so monomaniacally on quickly defeating Isis –defined as pushing it from overt control of cities rather than how Isis was defeated, the Coalition ignored wider conflict dynamics, especially in Syria, and countenanced partnerships, direct and indirect, with actors whose strength translated into political legitimacy for Isis. This allowed Isis's international appeal to be de-linked from its (increasing lack of) success on the battlefield in Iraq and Syria, and to transform into an international movement.

Moreover, long after Isis's statelet is dismantled – even if Isis is defeated for good, which seems open to doubt on present trends – the foreign networks have a life of their own and the online infrastructure of Amn al-Kharji will remain.

Second, in devising domestic counter-terrorism policy, western states should not over-invest in strategies that emphasise countering self-radicalization while they are confronting a problem, on this scale, of a foreign adversary being able to reach into their societies and direct their citizens against them. In some ways, this is an easier problem to solve: unlike true lone wolves, whose only pre-planning is in their own mind, this means there are interceptable communications, for example.

But it does also mean that dealing with the problem is not only an internal matter for governments.

Kyle W. Orton is associate fellow at the Henry Jackson Society and a Middle East analyst and commentator. Follow him on Twitter: @KyleWOrton