After an investigation the worker, believed to be a doctor, has been found to carry the disease, which may have been passed on during cardiac surgery.
As a result 351 patients who had contact with the worker are now being contacted by their GPs. The health authority has set up a help-line for worried patients.
It is the first time a patient has been infected by a health worker with hepatitis C, a form of the liver condition which may not produce symptoms for 20 to 30 years.
While some patients may be mildly affected, between 10 and 20 per cent will develop liver damage leading to liver failure or cancer. A liver transplant will be the only solution for some of these patients.
Hepatitis C is passed by blood-to-blood contact. Thousands of haemophiliacs and people who had blood transfusions before blood was treated have caught the disease. Between 1 in 100 and 1 in 1,000 people are believed to carry the hepatitis C virus.
The heart surgery took place a year ago at the London Chest Hospital. When the patient developed "acute hepatitis C" - with no other likely route of infection - the hospital set up an investigation and all health workers who had contact with the patient were tested.
In a statement the East London and City Health Authority said: "Every single patient who may be at risk of developing hepatitis C is currently being contacted individually. Because all the patients have been identified other patients at the hospital should not be worried. Current patients are not at risk and the hospital continues to operate as normal."
Patients will be offered testing. People with hepatitis C may be offered treatment with interferon, but this is only found to be effective in a quarter of patients.
The health worker from the London Chest Hospital is now on leave and will not take part in any further procedures, the health authority said.
There have been numerous cases of health workers, including doctors and dentists, carrying hepatitis B. They have stopped invasive procedures with patients as a result.
Over the last two years health workers have been vaccinated against hepatitis B. But there are no guidelines for screening workers for hepatitis C and no vaccine exists. Hepatitis B is more infectious than hepatitis C.
Alison Rogers, director of the charity British Liver Trust, said: "We are still astonished that hepatitis C has such a low profile. The problem is that there is no reliable information on prevalence of hepatitis C in the community.
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