A spokesman said: "Our understanding is that if that had been acted on it would have prevented (the malware attack)".
"Since the global coordinated ransomware attack on thousands of private and public sector organisations across dozens of countries on Friday, there have been no sustained new attacks of that kind", the NCSC said.
The spread of the virus slowed over the weekend but the respite might only be brief, experts have warned. The latest virus exploits a flaw in Microsoft Windows first identified by USA intelligence.
Home Secretary Amber Rudd is due to chair a meeting of the Government's emergency Cobra committee on Whitehall at 5pm on Monday.
The cyberattack has hit 200,000 computers in more than 150 countries, according to Rob Wainwright, the executive director of Europol, the European Union's police agency.
"It seems inconceivable that organisations such as the NHS are prepared to jeopardise highly confidential patient data or critical infrastructure through inadequate cyber security that relies heavily on out-dated anti-virus technologies, when effective alternatives like file-regeneration are available".
Nevertheless, the attack hit 48 NHS Trusts, and a number are still affected, including London's Barts Health NHS Trust, which runs The Royal London Hospital, Newham Hospital, Whipps Cross Hospital, Mile End Hospital and St Bartholomew's Hospital.
This week NHS bosses and the Government were facing questions over why hospitals and Global Positioning System had been left vulnerable.
Smith's blog post did not address another factor in the ransomware's spread, one that hints at the difficulty of uniting against a hacking attack: Users of pirated Microsoft software are unable to download the security patch, forcing them to fend for themselves or rely on a third-party source for a solution.
"Then first thing people should be doing (before checking email) when they got to their office this morning is updating their operating system, the Windows operating system, because that is the only thing that is going to protect them against this".
But Prime Minister Theresa May has rejected claims the Government ignored warnings the health service was vulnerable, and said the Government was putting £2bn into cyber security.
Queen Alexandra Hospital in Portsmouth was unaffected by the attack.
Another method, which preys on machines using outdated software, is visiting a malicious site.
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