"It is going to spread far and wide within the internal systems of organizations - this is turning into the biggest cybersecurity incident I've ever seen", UK-based security architect Kevin Beaumont said.
The Spanish energy ministry said it had "confirmation of various cyber attacks targeting Spanish companies", adding that the attackers used ransomware which blocks access to files until a ransom is paid.
"The investigation is at an early stage but we believe the malware variant is Wanna Decryptor", the NHS says, referring to software that is being blamed for a number of ransom attacks Friday.
A window appeared on screens of infected computers that demanded payment with the digital currency bitcoin in order to regain access to files, a Telefonica spokesman said.
As almost 45 NHS organisations from London to Scotland were hit in the "ransomware" attack on Friday, patients of the state-funded countrywide service faced chaos as appointments and surgeries had to be cancelled.
The BBC understands up to 39 NHS organisations and some GP practices have been affected.
The minister said lessons had to be learned from the attack.
Wainwright said Europol had been concerned about cyber security in the healthcare sector, which deals with a lot of sensitive data, but declined to comment on whether Britain's National Health Service had been adequately funded.
The East and North Hertfordshire NHS trust updated its website shortly after the attack, telling visitors that they were "currently experiencing significant problems with our IT and telephone network".
"This is not targeted at the NHS, it's an global attack and a number of countries and organisations have been affected", May said, referring to the country's National Health Service.
However, there have been some reports of ambulances being diverted from affected hospitals and individual NHS trusts have asked registered patients not to attend unless it is urgent.
Staff can not access patient data, which has been scrambled by ransomware.
Bart's Health, which runs several London hospitals, said it had activated its major incident plan, cancelling routine appointments and diverting ambulances to neighboring hospitals.
At the Royal London Hospital operations were cancelled and staff were ordered not to touch their computers.
The infections have disabled more than a dozen hospitals in the United Kingdom, Spain's largest telecom company and universities in Italy as well as some FedEx computers.
"Our society increasingly relies on interconnected systems to deliver key services such as health", he said.
Hospitals across England reported the attack was causing huge problems to their services.