In total 47 organisations reported being affected by the cyber attack and the disruption will continue into the new working week.
Asked if warnings had been ignored, Mrs May said: "No".
Barts Health, which runs five London hospitals, says it is still sending some ambulances to other hospitals and has canceled some surgeries and outpatient appointments.
"It is important to understand that the way these attacks work means that compromises of machines and networks that have already occurred may not yet have been detected, and that existing infections from the malware can spread within networks", said the U.K.'s National Cyber Security Centre in a statement Sunday.
Meanwhile, automaker Renault decided not to reopen a 3,500-employee plant in France on Monday as a "preventative step".
The Nissan vehicle plant in Sunderland is still suffering from issues caused by the ransomware attack which forced auto production to a halt on Friday night.
They should do this before they open their emails or other programs.
On social media, students complained about not being able to access their work, and people in various cities said they hadn't been able to take their driving tests because some local traffic police systems were down.
Flexera published research showing nearly 9.9 per cent of Australian PC users had unpatched Windows operating systems in the first quarter of 2017, which was worse than the 7.5 per cent last quarter and 5.9 per cent this time past year.
The recent cyberattack targeted government, businesses and hospitals. They were installing software to fix the problems.
At least one strain of the ransomware has proven especially vicious. It spread cyber chaos worldwide, hitting Britain's hospital network, Germany's railway and scores of companies and government agencies.
Microsoft on Sunday said a software vulnerability stolen from the U.S. National Security Agency has affected customers around the world, and described the spread of the WannaCrypt ransomware on Friday in many countries as yet another example of the problems caused by the stockpiling of vulnerabilities by governments.
"Of course there are amounts that are being demanded, in this case relatively small amounts - $300 rising to $600 if you don't pay within three days", he said. The weakness in cyber security makes the country vulnerable to many other criminal activities that have been facilitated by the internet. It was restoring its advertising servers at dozens of theaters after the attack left the company unable to display trailers of upcoming movies. Its movie ticket systems were unaffected.
Symantec said the majority of organisations affected were in Europe.
Cybersecurity experts say the unknown hackers who launched this weekend's "ransomware" attacks used a vulnerability that was exposed in NSA documents leaked online. First discovered on May 12, the cyberattack has created havoc around the world. It affected the UK's National Health Service, Russia's ministry of interior, China government agencies, Deutsche Bahn, vehicle makers Nissan and Renault, PetroChina, logistics giant FedEx, and other company and hospital computer systems in countries from Eastern Europe to the USA and Asia.
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