A healthcare worker at Worthing Hospital is among the eight confirmed cases of coronavirus in the UK.
Staff at the West Sussex hospital received a memo on Tuesday telling them a member of staff working in the A&E department had been diagnosed with the virus.
A spokeswoman for the Department of Health said that all services at the hospital, including surgery and outpatients, are operating normally.
It is understood the healthcare worker at Worthing Hospital is not the same person as the locum doctor working in Brighton, who is also one of the eight cases.
Meanwhile, two prisoners at HMP Bullingdon in Oxfordshire are being tested for the illness and are being held in isolation.
Access to one of the wings of the Category B prison has been restricted, and one of the men is understood to have been recently transferred from a Thai jail.
They are both reported to be suffering flu-like symptoms.
As of Tuesday evening, a total of 1,358 people have been tested for coronavirus in the UK, of which 1,350 were confirmed negative and eight positive, the Department of Health said.
On Tuesday, the Prime Minister praised the response of the NHS and said anyone concerned should “simply follow their advice”.
Speaking in Birmingham, Mr Johnson said: “We are a great country, we have got a fantastic NHS, we have got fantastic doctors and advice, and they should simply take the advice of the NHS.
“People have every reason to be confident and calm about all that kind of thing… all the coronavirus, and any threats from disease.”
It came as Steve Walsh, the businessman at the centre of a UK outbreak of coronavirus, thanked the NHS for his treatment and said he is “fully recovered”.
Mr Walsh, 53, from Hove in East Sussex – who is still in quarantine at St Thomas’ Hospital in London, picked up coronavirus while at a conference in Singapore.
On his way back to the UK, he stopped off for several days at a French ski chalet, where five Britons were subsequently infected with the virus.
He is also linked to at least five further cases of coronavirus in the UK, including the doctor working at the Brighton surgery.
A source told the PA news agency that the doctor, acting as a locum at County Oak Medical Centre, had only carried out one day of admin work there recently and had not had any direct contact with patients.
On Wednesday morning, the surgery said it had re-opened with a “limited service”
A statement on the website for County Oak Medical Centre – operator of previously closed Warmdene and Carden surgeries – told patients that the facilities have been “extensively and rigorously cleaned throughout”.
Meanwhile, Patcham Nursing Home said on Tuesday that it has “closed to all visitors” after one of the infected GPs visited a patient there about a week ago.
A spokeswoman for the care home said no one was unwell and the closure was a precaution.
Mr Walsh is also linked to one male patient who was taken ill in Majorca.
Speaking from hospital on Tuesday, Mr Walsh, a cub scout leader, said in a statement: “I would like to thank the NHS for their help and care – whilst I have fully recovered, my thoughts are with others who have contracted coronavirus.
“As soon as I knew I had been exposed to a confirmed case of coronavirus, I contacted my GP, NHS 111 and Public Health England.
“I was advised to attend an isolated room at hospital, despite showing no symptoms, and subsequently self-isolated at home as instructed.
“When the diagnosis was confirmed I was sent to an isolation unit in hospital, where I remain, and, as a precaution, my family was also asked to isolate themselves.”
A spokeswoman for the Scout Association said Mr Walsh had not been to any Scout meetings since his return to the UK, and wished him a quick recovery.
Also on Tuesday, Health Secretary Matt Hancock told MPs in the Commons that new funding was being launched immediately “to support any urgent works the NHS needs for the coronavirus response, such as the creation of further isolation areas and other necessary facilities”.
Meanwhile, pupils at several Brighton schools were told they could stay at home after reports that some teachers and families feared they had come into contact with the virus.
Earlier, Dr Tedros Ghebreyesus, director-general of the World Health Organisation, described the outbreak as “a very grave threat for the rest of the world”.