According to news reports a GP practice in Brighton has been temporarily closed after a staff member tested positive for coronavirus.
Patients at the city's County Oak medical centre have been advised to contact the NHS 111 phone service if they have concerns. Two of the eight people diagnosed in the UK are understood to be GPs.
The Department of Health has called the virus a "serious and imminent threat" to public health, but the overall risk to the population is "moderate".
However, the risk to individuals is low, the department said.
A school in Southampton has also closed over concerns about the virus. St Mary's Independent School said the "precautionary" three-day closure came after "members of the school community" became ill, having recently travelled to China.
In Northamptonshire Brackley Medical Centre was also closed as a precautionary measure, but later reopened.
According to the BBC four new UK cases were announced on Monday - taking the total number of people infected in the UK to eight.