The students from Thomas’s Battersea in southwest London were understood to have been sent home as they await test results for the deadly bug.
Two of the children are said to have reported flu-like symptoms after returning from a trip to coronavirus-hit northern Italy, Spanish news site El Confidencial reports.
The school, where both Charlotte and George are pupils, is one of more than 40 affected by the coronavirus, which has so far killed more than 2700 people around the world.
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Thomas’s said in a statement, reported on the Spanish site: “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.
“All parents have been informed and we have maintained regular communication with our school community to ensure that councils are shared and important information circulated.
“Of course, we will preserve the confidentiality of staff and students, and we will not comment on specific cases.”
The school is said to have sent out emails to parents advising them four pupils are being assessed for symptoms.
George, six, is now in year 2 at the school while four-year-old Charlotte started reception class in September.
Prince William and Kate Middleton said previously the school was chosen for George because “it was the right fit for him”.
Established by David and Joanna Thomas 40 years ago, Thomas’s Battersea has described itself as being “happy, dynamic and vibrant” and a school that prides itself on its “excellent academic results”.
There are now 29 schools in coronavirus lockdown after pupils returned from ski trips during the half term in Italy – where 11 people have now died as the number of cases continues to rocket.
The Italian Government has put 11 towns in Lombardy and Veneto – both popular skiing destinations – into lockdown.
One school axed its ski trip over fears of the deadly virus, with pupils travelling back to the UK two days earlier than planned.
A further 16 schools in the UK sent staff and pupils home to self-isolate for 14 days.
Also British people who have travelled to Italy have today been told to “self-isolate” for 14 days.
This article originally appeared on The Sun and was reproduced with permission