"Like all schools we are taking the potential risks connected with the spread of Covid-19 very seriously and to this end are following government guidance to the letter around both prevention against infection and in dealing with cases where any staff or pupils are suspected of being exposed to the virus or who display any symptoms," the spokesperson said in a statement. "We currently have a very small number of pupils who have been tested and these individuals are currently, as per government advice, remaining at home pending the receipt of their test results."
George, 6, is in his third year at Thomas's Battersea and Charlotte, 4, started her first year at the school last fall.
Thomas's Battersea has informed parents, including William and Kate, about the coronavirus testing and is not commenting on specific cases to "preserve staff and pupil confidentiality," according to the spokesperson.
The newly identified virus, known officially as COVID-19, originated in the Chinese city of Wuhan back in December and has since spread overseas to 49 other countries, with South Korea, Italy and Iran seeing recent surges in case numbers. The World Health Organization, which has declared the outbreak a global health emergency and said it "absolutely" has the potential to become a pandemic, has recorded more than 81,000 confirmed infections globally. Over 96% of those cases were in China.
At least 2,762 people have died from confirmed cases of the virus, all but 44 in China, according to the latest data from the WHO.
COVID-19 causes symptoms similar to pneumonia, ranging from the mild, such as a slight cough, to the more severe, including fever and difficulty breathing, according to the CDC. There is no vaccine yet for the virus.
Increasing concerns over virus exposure have prompted some airlines to suspend flights to China and South Korea and cities around the world to suspend public gatherings and close schools, businesses and restaurants. Japanese Prime Minister Shinzo Abe on Thursday ordered the closure of all schools nationwide to help control the spread of the disease.
More than one dozen people have tested positive for coronavirus in England.
ABC News' Morgan Winsor and Erin Schumaker contributed to this report.