The U.K. National Health Service (NHS) was among the worst hit organisations, forcing hospitals to cancel appointments and delay operations as they could not access their patients' medical records.
Experts and authorities have told users, if hit, to not pay the attackers' ransom.
In a statement it said: "East Kent Hospitals unaffected by yesterday's cyber attack".
The press release adds that the police, industrial authorities and the sectors of computer technology, education, banking and cyber-space, as well as some computer security companies, have already taken measures to respond to the attack.
A total 12 out of 14 health boards in Scotland experienced only minor disruptions following Friday's global ransomware attack, with two escaping the attack completely.
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Australian organisations will return to work as the local fallout from the weekend's global cyber attack becomes clearer.
The ransomware attack has been described as the largest-ever of its kind.
"It's why we are putting £2 billion [$2.6 billion] into cyber-security over the coming years and, of course, created the National Cyber Security Centre".
Barts Health, which runs the hospital, was among a fifth of the country's NHS trusts to have its computers infected by ransomware.
"They have been working I know through the night nearly to make sure patches are in place to make sure that hopefully the NHS services can get back to normal", he told BBC radio.
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There was no loss of data or any impact on other services, the hospital confirmed.
"I would warn patients, if they made an appointment or anything else on Friday, there is a good chance it hasn't been logged, so I would urge them to contact us again".
But Prime Minister Theresa May has rejected claims the government ignored warnings the NHS was vulnerable to a possible attack.
Brad Smith, Microsoft president and chief legal officer, said: "We have seen vulnerabilities stored by the Central Intelligence Agency show up on WikiLeaks, and now this vulnerability stolen from the NSA has affected customers around the world".
Ransomware cyber-attack a wake-up call, Microsoft warns
The other is to disable a type of software that connects computers to printers and faxes, which the virus exploits, O'Leary added. The most important thing we can do right now is to be in touch with them, and to offer reassurance and guidance as appropriate.