Home Secretary Amber Rudd will chair a meeting of the Government's emergency COBRA committee later.
The attack has hit more than 75,000 computers in 99 countries.
Yesterday, Jeremy Hunt told the BBC the National Crime Agency was investigating the incident that saw NHS computers locked down and money demanded from the attackers to unlock the files.
Microsoft has issued a blistering attack on the United States government after a software vulnerability stockpiled by the National Security Agency (NSA) paralysed NHS hospitals and thousands of other organisations around the world.
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Digital managers in Britain had been bracing themselves Monday for a possible second cyber attack, but in the event there was no new attack. "Staff are working hard to ensure that the small number of organisations still affected return to normal shortly".
However some hospitals are still suffering disruption from the cyber attack, which hit 200,000 victims across 150 countries around the world.
Pictures posted on social media showed screens of NHS computers with images demanding payment of 300 USA dollars worth of the online currency Bitcoin, threatening to delete files within seven days.
York Teaching Hospital NHS Foundation Trust said some out-patient appointments had been cancelled on Monday, especially at Selby War Memorial Hospital, but most were not affected. Questions have been raised over Trident's vulnerability to potential cyber attacks, as the system is believed to use ageing Window's XP software - the same operating system targeted by the global ransomware attack.
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He added: "We will provide a public update should the situation change".
John Clark, professor of computer and information security at the University of Sheffield, said the attack should act as a wake-up call for the health service and for businesses and individuals to defend themselves adequately against so-called "ransomware".
'It's an worldwide attack and a number of countries and organisations have been affected, ' British Prime Minister Theresa May said.
"In particular, making sure that our data is properly backed up and making sure that we are using the software patches, the anti-virus patches, that are sent out regularly by manufacturers".
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The Nintendo Switch sold 280,000 units in the region, making it the top hardware choice among Americans in the month of April. As for the starting positions in the game, they have been changed according to the order in which players join the game.