As well as the computer admin system, services crucial to front-line work including X-rays and doctor bleep systems have been affected.
However, there are no reports of the hack compromising vital systems such as life support machines.
Earlier today, the same ransomware hit Telefonica – the owner of O2 – and other huge organisations in Spain.
There were also reports of mass computer infections in Italy, Portugal, Russia, Vietnam, Kazakhstan and Taiwan.
In addition to the hospital computers holding patient records, the devices affected included MRI scanners, blood fridges and operating theatre equipment.
Yesterday hospital trusts including Barts Health in London and Colchester General in Essex were advising patients to stay away unless they needed “essential” treatment and cancelled hundreds of appointments and operation.
"This attack was not specifically targeted at the NHS and is affecting organisations from across a range of sectors.
"Our focus is on supporting organisations to manage the incident swiftly and decisively, but we will continue to communicate with NHS colleagues and will share more information as it becomes available." In a statement Theresa May said patient data "is safe".
"NHS Digital is working closely with the National Cyber Security Centre, the Department of Health and NHS England to support affected organisations and to recommend appropriate mitigations.Last night patients were urged to stay away from GP practices this morning as the chairman of the Royal College of GPs said the hack attack had an "extensive impact".Dr Helen Stokes-Lampard said: “The concern is that on Monday morning the appointment system may not be working, some places may not be able to access routine results, even the phone lines in some cases may not be working.IT concerns include interoperability, vendors, innovation, nursing voice, education, and collaboration. One identified interest area was the EHR, which was seen by nurses as both a benefit and a source of considerable frustration.Furthermore, nurses were challenged to articulate their concerns due, in part, to the fact that there was no available taxonomy to describe EHR-related difficulties.