Security Minister Ben Wallace has said that NHS trusts have enough funds to protect against cyber-attacks, and that the "real key" was in regularly backing up data and installing security patches.
A computer virus known as WannaCry or WannaCrypt has so far spread more than 150 countries, including Turkey, but showed signs of slowing down on Monday.
Shadow health secretary Jon Ashworth, in a letter to Mr Hunt, said concerns were repeatedly flagged about outdated computer systems and he accused the Government of "raiding" NHS capital budgets to fund day-to-day spending.
"In addition to protective real-time monitoring of national NHS IT services and systems, which were unaffected by this issue, we are supporting NHS organisations by undertaking cyber security testing and providing bespoke advice and action points".
They should immediately update their Windows operating system and back up their data.
"Many of those victims were businesses, including large corporations".
"We have recently invested in upgrading IT to protect potentially vulnerable NHS Wales systems and all GP systems in Wales are managed and supported centrally, with best practice security controls". The cyberattackers demanded payments of $300 or more from users to unlock their devices. Seventy-four countries, including the UK, US, China, Russia, Spain, Italy and Taiwan, reported having the virus.
The North West Anglia NHS Foundation Trust, which runs Peterborough City Hospital, Stamford and Rutland Hospital and Hinchingbrooke Hospital, was not hit by the attack, but it temporarily took its website down as a precautionary measure.
On Sunday night, Microsoft blamed the USA spy agency that had originally developed software that allowed the ransomware attack to infect computers.
Microsoft released patches last month and on Friday to fix a vulnerability that allowed the worm to spread across networks.
"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". Experts say the attackers have made just over $51,000.
How can you tell if a computer has been infected?
"We will get a decryption tool eventually, but for the moment, it's still a live threat and we're still in disaster recovery mode", the report quoted Europol Director Rob Wainwright as saying.
Company president and chief legal officer Brad Smith in a blog post criticized what he called the "stockpiling" of unsafe software code by governments which could be exploited by hackers.