Europol says Friday’s cyberattack hit 200,000 victims in 150-plus countries and warned there may be many more.
Director Rob Wainwright spoke as hospitals in the UK were beginning to get back to normal although some were still experiencing problems after the global attack which hit 48 NHS trusts in England and 13 Scottish health boards.
His comments also came as security experts warned that further cyberattacks are likely.
Mr Wainwright said: «At the moment, we are in the face of an escalating threat. The numbers are going up. I am worried about how the numbers will continue to grow when people go to work and turn on their machines on Monday morning.
«The global reach is unprecedented. The latest count is over 200,000 victims in at least 150 countries, and those victims, many of those will be businesses, including large corporations.»
Mr Wainwright said the attack was indiscriminate, fast-spreading and unique because the ransomware was being used in combination with a worm which means the infection of one computer could automatically spread it through a whole network.
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Few banks in Europe were affected after learning from previous experiences of attacks, Mr Wainwright said but an attack on public health systems, which badly affected the NHS, had caused concern.
He said: «We have been concerned for some time that the healthcare sectors in many countries are particularly vulnerable. They’re processing a lot of sensitive data.»
Mr Wainwright said Europol was working with the FBI to track down those responsible and said it was likely more than one person was behind the attack but he said identifying offenders was «very difficult».
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«We’re in a very difficult fight against these ever more sophisticated cyber crime syndicates that are using encryption to hide their activity, » he said.
The attack is still causing problems in some hospitals.
Barts Health NHS Trust, the largest NHS trust in the country, has said it was continuing to experience IT disruption, leading to delays and cancellations for patients.
It has advised the public to use other NHS services where possible.
Cyber security expert Dr Markus Jakobsson, chief scientist at the cyber security firm Agari, has told Sky News there is «no reason» why the hackers would not launch another attack and warned: «It’s going to be another tough week».
He said the malware strike had been shut off «temporarily», but added: «There is no reason why the attacker won’t come back and decide to pull another one on us all.
«It’s going to be another tough week I think.»
He stressed the importance of organisations taking action to safeguard their data.
Dr Jakobsson said: «There’s absolutely no excuse for any business not to have up to date systems. This is critical.»
He added: «The real problem is that there’s the human factor.
People are making mistakes. Whether it’s about not patching things like in this situation or clicking on things in emails.
«And the attackers know this very well and they take advantage of it in a very clever way.
«Psychology is against us in a sense.»
He went on: «This is a watershed event and we need to fear what this will do to the trust of the infrastructure.»
Meanwhile Defence Secretary Michael Fallon has insisted that Britain’s nuclear deterrent is protected from cyberattacks.
Sir Michael dismissed concerns over the threat of viruses on Trident operating systems.
He said the Government had set aside more than £1.9bn to tackle cyber threats, including £50m that went to the NHS, after an official security review highlighted hacks as a major threat.
Sir Michael told the BBC’s Andrew Marr Show: «We never comment on the different systems, obviously for reasons of security, that our submarines use but our Vanguard submarines I can absolutely assure you, are safe and operate in isolation when they are out on patrol, and I have complete confidence in our nuclear deterrent.» More follows…
