Such programs stop users from accessing their files until they make a payment in Bitcoin.
Security experts have warned that another attack is imminent, most likely on Monday, and could be unstoppable.
United Lincolnshire Hospitals Trust has said all patients should attend their booked outpatient appointments and operations "as planned tomorrow (Tuesday) after 'significant progress" has been made in restoring IT systems following Friday's cyber attack.
The WannaCry ransomware attack affected more than 230,000 computers in 150 countries.
Capitalising on spying tools believed to have been developed by the U.S. National Security Agency, the virus dubbed WannaCry has blocked more than 200,000 computers across the globe, demanding a ransom to unlock them.
Later on Friday, it was revealed that the attack had spread to 75 countries, hitting Russia's interior ministry, the Spanish telecom giant Telefonica and the USA delivery firm FedEx.
"With access to and the use of vast quantities of personal data, public bodies must have in place robust data protection plans, ensure access to expert support and not to cut cyber security resources when efficiencies are needed elsewhere".
Cyber-security firm Avast reportedly said it had seen 75,000 cases of the ransomware around the world.
An NHS update for the North East and North Cumbria said its primary care computer network was switched back on yesterday afternoon, with practices back up and running this morning.
Health Secretary Jeremy Hunt confirmed there had not been a second wave of attacks on NHS trusts and said it was "encouraging" that the level of criminal activity was at "the lower end of the range" anticipated.
Twitter users around the world posted complaints about their computers shutting down and posted photos of the ransom demands on their computer screens.
The ransomware attack has been described as the largest-ever of its kind. The attack was so overarching that it even affected notably older iterations like Windows XP and Windows Server 2003, forcing the company to release updates to address now-obvious vulnerabilities.
Later, he admitted that he wasn't aware registering the domain would halt the spread of the attack, which has seen him branded an as "accidental hero".
Because the attack occurred on Friday, right before people left their offices and went home for the weekend, many computers weren't affected because they simply weren't in use.