The Duke of Cambridge admitted his week has been "very interesting" as a woman remained in police custody on suspicion of trying to break into Prince George's school.
The four-year-old, who started school last week, was back at Thomas's Battersea on Thursday morning as his father toured the Aintree University Hospital in Liverpool at the start of a day of engagements in Merseyside.
A 40-year-old woman remains in custody following her arrest on Wednesday, the day after she allegedly tried to get inside the south London school.
The woman was reportedly detained by undercover police officers in a square just 100 yards from the school.
Speaking to patient Pagan Tordengrav, 55, William said the Duchess of Cambridge was doing "very well", adding: "And George is at school.
"It's been a very interesting week."
Describing the woman's arrest one eyewitness, who was sitting in a nearby restaurant, told the Daily Mail: "She was just sitting there really quietly with two men in ordinary clothes either side of her.
"She was completely calm and passive. She was completely unfazed."
George was driven into school through a side entrance on Thursday morning by two members of staff.
Along with his cohort, the prince is currently attending reception classes on a half-day basis and building up to staying for lunch.
Several plain-clothed officers have been spotted in the area surrounding the fee-paying school, where security is being reviewed following the scare.
The incident came less than a week after George's first day on September 7.
A police spokesman said they were working with the school to review its security arrangements after the incident.
Thomas's Battersea educates 560 boys and girls aged from four to 13, with around 20 pupils in each class.
Fees cost £17,604 a year, and increase to £19,884 a year for those in year three and above.