The BBC understands that the two men were observed by both private security and school staff, stopping at various points and looking into the school grounds, before returning to a van which police later established was a rental vehicle.
One of the men was later identified to be an international photographer is believed to work for a known European press agency.
“The decision by photographers to conduct themselves in this way around a school is extraordinarily reckless,” Harry and Meghan’s spokesman said.
“There is a world of difference between legitimate media activity and photographers walking the perimeter of a school, stopping to look into the grounds and monitoring children as they go about their day.”
The spokesman continued: “Whatever photographs they may have been seeking, this was not only an unacceptable intrusion into the privacy of children; it was an irresponsible and ill-considered way to conduct themselves in the vicinity of a school.”
The children began school in the UK at the start of September, but changed after a few days after security concerns were raised about traffic during the school run.
Earlier this month, it emerged that the Sussexes are going to be given a review of their publicly funded security, following their move back.