Last Friday's outbreak of the WannaCry ransomware infected hundreds of thousands of computers worldwide, including thousands at United Kingdom hospitals.
Some GPs are asking people to consider whether they really need appointments.
However some hospitals are still suffering disruption from the cyber attack, which hit 200,000 victims across 150 countries around the world.
The extortion attack, also called ransomware, used "WannaCry" malware that encrypts users' files until users pay a ransom.
The WannaCry attack on Friday has affected 47 NHS organisations, some of which were still experiencing problems on Monday, although the health secretary, Jeremy Hunt, said a feared second wave of attacks on the health system had not occurred.
A statement released by Lancashire Teaching Hospitals - whose hospitals include Preston and Chorley - said: "The worldwide cyber attack has affected the IT systems at Lancashire Teaching Hospitals NHS Foundation Trust".
He told BBC News that he had been briefed on Monday morning by GCHQ and the National Security Cyber Centre, after he had been accused of not discussing the subject or giving comments to reporters over the weekend.
Government ministers were due to hold an emergency response meeting later on Monday to deal with the crisis.
"It is thanks to the dedication and hard work of many staff, who worked unstintingly throughout the weekend, came in early this morning and are staying late tonight that we have minimised the effect on patient care".
Mr Biggs said: "It is vital that NHS trusts invest adequately in cyber security as they seek to protect themselves against future attacks".
"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".
"They have been working I know through the night nearly to make sure patches are in place to make sure that hopefully the NHS services can get back to normal", Wallace told BBC Radio.
The government is insisting that the NHS had been repeatedly warned about the cyber-threat to its IT systems.
In a statement it said: "East Kent Hospitals unaffected by yesterday's cyber attack".
But Opposition parties have criticised the government, saying they had cut funding to the NHS IT budget and a contract to protect computer systems was not renewed after 2015.
"The Health Secretary has been working round the clock on co-ordinating the NHS response to this, which has been a hugely impressive response".
This prevented access to records and caused chaos throughout the NHS.
She asked people to think about their needs before heading to hospital or the GP surgery.
How has Monday been so far?
Hospitals have stopped diverting patients following last week's cyber attack which crippled many NHS Trusts' IT systems. So what made our hospitals so vulnerable?
Worse, the malware was able to create so much chaos because it was designed to self-replicate like a virus, spreading quickly once inside university, business and government networks.
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