However some hospitals are still suffering disruption from the cyber attack, which hit 200,000 victims across 150 countries around the world.
Europol, the EU's law enforcement agency, says the number of targets who paid up is low.
The virus also has a wormlike features that looks for other vulnerable systems once it's embedded in your computer, which means it can spread to other computers in a network.
Europol Director Rob Wainwright told a British television program the attack was unique in that the ransomware was used in combination with "a worm functionality" so the infection spread automatically.
A spokesperson from Hampshire Hospitals NHS Foundation Trust said: "We can confirm that the radiology services affected by the national cyber-attack at Basingstoke and North Hampshire Hospital have been restored".More news: Alexis Sanchez states his prediction for Arsenal v Chelsea
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In the United Kingdom more than 50 hospitals, doctor surgeries and pharmacies were targeted, Germany's rail network Deutsche Bahn was attacked, and Russia's Interior Ministry was infected with the malware.
A spokesman said: "Our understanding is that if that had been acted on it would have prevented [the malware attack]".
"As people return to work tomorrow after the weekend, many will have unopened, potentially infected emails in their inboxes, or their systems may already be infected and are waiting to activate".
SHANGHAI-"Hundreds of thousands" of Chinese computers at almost 30,000 institutions including government agencies have been hit by the global ransomware attack, a leading Chinese security-software provider has said, though the Asian impact has otherwise been relatively muted.
Investigators are working to hunt down those responsible for the Wanna Decryptor ransomware, also known as WannaCry, which encrypts files on a user's computer, blocking them from view and threatening to delete them unless a payment is made. Microsoft released a patch over the weekend for the Eternal Blue vulnerability that defends against it even with older versions of Windows.
The UK security researcher "MalwareTech", who helped to limit the ransomware attack, predicted "another one coming. quite likely on Monday", the BBC reported.