Four pupils at Prince George and Princess Charlotte's London school are in isolation over fears they may have contracted the deadly coronavirus.
The children from Thomas's Battersea are self-isolating at home and waiting on test results after their return from a school trip to northern Italy.
Two children came home early after developing flu-like symptoms.
The news comes as schools across the UK close over fears of a widespread outbreak and countries across Europe see their numbers of infections grow.
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The Spanish newspaper El Confidencial published a statement from the school:
"Like all schools, we are taking very seriously the potential risks related to the spread of Covid-19 and to this end we are following the Government's instructions to the letter on infection prevention and case management in which it is suspected that some staff member or students exposed to the virus or showing any symptoms.
'We currently have a very small number of students who have been evaluated and these individuals currently remain in their homes waiting to receive the results of their exams".
The statement also said that it would "preserve the confidentiality of staff and students and would not comment on specific cases".
Speaking on Radio 4, Professor Paul Cosford said: "I think you have to be cautious about the idea of closing down communities, towns, and so on.
"But what will happen is when we see - if we do get to the position of a more widespread infection - we will monitor that as it develops.
"We will take the best scientific advice to how we may be able to delay transmission further and if that includes actions to isolate more widely then of course we will do that.
"But I think at the moment this is unlikely."
Cosford's comments come as a leaked report suggest that up to 500,000 could die from the virus in the UK if it infects up to 80 per cent of the population.
The scenario was described as a "reasonable worst case" in the briefing to ministers, which was leaked to the Sun newspaper.
Schools across the country have closed because of the risk posed by staff and pupils who have travelled overseas during the half-term break.
Many of those schools had organised skiing trips to northern Italy, where the virus is spreading quickly and the death toll has reached 12.