A 40-year-old woman is under arrest after allegedly trying to break in to the school in south London where Prince George is a student, the Metropolitan Police said Wednesday.

The incident took place Tuesday at Thomas's Battersea School, an independent fee-paying school with a yearly tuition of £17,604 ($23,000). The woman was arrested Wednesday afternoon and remains in custody, police said.

The Metropolitan Police, which is part of the protective security arrangements for the prince, said it is working with the school to review its security after the incident. Police said the school "is responsible for building security on its site."

It was not immediately clear if school was in session when the incident happened. A police spokesman said the arrest followed an incident in which "an individual gained access to (the school's) premises."

The 4-year-old prince's first day of schoolwas last Thursday, and he arrived holding the hand of his father, Prince William. His mother, the Duchess of Cambridge, was not able to accompany him because she is suffering from hyperemesis gravidarum, which involves nausea and vomiting more severe than the typical morning sickness many women suffer during early pregnancy.

Kensington Palace announced September 5 that the royal couple is expecting a third child.

The Thomas's Battersea School has been described as "a big, busy, slightly chaotic school for cosmopolitan parents who want their children to have the best English education money can buy," according to the UK Good Schools Guide.

A spokeswoman for Kensington Palace told CNN it was "aware of the incident" but wouldn't comment on security matters.