The Duke and Duchess of Cambridge have released a strong warning to paparazzi to stop harassing their children.

The communications secretary for Kensington Palace has written an open letter to the media, highlighting how Prince George and Princess Charlotte are increasingly under surveillance from unauthorised photographers.

The letter praised British, Australian, Canadian and New Zealand media for respecting the family's privacy, adding: "The Duke and Duchess are glad that leaders in the media industry share the view that every child, regardless of their future public role, deserves a safe, happy, and private childhood."

Thanking the public for messages of support, they also promised that official opportunities to photograph the children would become "a regular occurrence" as they grew older.

They are still "upset" that "a small number of paparazzi photographers" are going to extreme lengths to satisfy a large international market for unauthorised photos of the children, however.

They said long lenses had been used to capture images of the Duchess and Prince George in private parks and to monitor George, his nanny, household staff and visiting children.

They said cars leaving the family's homes had been followed and other children had even been used to lure the young prince into the view of photographers while playing in playgrounds.

The letter said that, like most parents, the couple enjoyed sharing photos of their children, but added that every parent would object to anyone - particularly strangers - taking photos of their children without permission.

"Every parent would understand their deep unease at only learning they had been followed and watched days later when photographs emerged," it added.

The letter added that George is currently that market's "number one target" and the decision had been made to "discuss" this as incidents became "more frequent and the tactics more alarming".

One incident last week was described as "disturbing but not at all uncommon".

A photographer had rented a car and parked in a discreet location outside a children's play area.

Concealed by darkened windows, he also hung sheets inside the vehicle and created a hide stocked with food and drinks to get him through a full day of surveillance, waiting in hope to capture images of Prince George, the palace said.

Police discovered him lying in the boot of the vehicle trying to take photos with a long lens through a small gap in his hide.

The palace's letter added: "It is of course upsetting that such tactics – reminiscent as they are of past surveillance by groups intent on doing more than capturing images – are being deployed to profit from the image of a two-year old boy.

"In a heightened security environment such tactics are a risk to all involved. The worry is that it will not always be possible to quickly distinguish between someone taking photos and someone intending to do more immediate harm."

Kensington Palace has said that legal steps are being taken to safeguard the family but they hope the letter will encourage public debate and help publishers of unauthorised photos of the children to understand the power they hold to "starve this disturbing activity of funding".