The region's NHS is keen to reassure people that the majority of services are running, however there has been disruption for some planned patient care.
The PM's spokesman said Government officials were meeting during the day to guide the response to the attack, and added he was not aware of any additional problems coming to light as staff returned to work.
There is no evidence that patient data has been compromised in the hack which affected around 1% of computers in the NHS in Scotland, the Scottish Government said.
Concerns were raised more NHS services could be affected on Monday, but Kent's hospital trusts confirmed they had not been targeted in the scam, thought to have accessed computers via email.
Bay Medical Group executive practice manager Kim Jones said: "It hasn't affected us at all, it has had hardly any impact".
Dr Wrigley spoke out after the cyber attack which brought parts of the NHS into chaos on Friday.
The Streamside Surgery practice, which is based at Thornbury Health Centre, was affected by the attack on Friday.
In Australia, Alistair MacGibbon, special advisor to Prime Minister Malcolm Turnbull on Cyber Security, said some small businesses would likely be hit "but as a whole of nation we can be confident, so far, that we have missed the worst of this".More news: Times Square crash victim was 18-year-old Michigan woman
The organisation also recommended that trusts ensure security software patches were up-to-date and that up-to-date virus software was also being used.
The Ministry of Electronics and Information Technology (MeitY) had said yesterday that a few systems of the Police Department in Andhra Pradesh were impacted and that the state government has been informed to follow the advisory by the CERT-In.
"They were in for more than 10 hours on Sunday working to get our computers up-and-running".
"These alerts included a patch to protect their systems".
More than 200,000 victims in around 150 countries have been infected by the ransomware which originated in the United Kingdom and Spain on Friday, before spreading globally. "This guidance was also reissued on Friday following emergence of this issue".
While many trusts across Yorkshire were unaffected, some were forced to suspend internet access to staff and block incoming external emails until software patches, which update a computers' immunity' were deployed.
Asked if warnings had been ignored, Mrs May said: "No". That's why the government, when we came into government in 2010, put money into cyber security.
The attack struck at least 16 British National Health Service organisations, along with computer networks of companies and municipalities in dozens of other countries.