Work is expected to begin on excavating the basement extension in September, despite a borough-wide ban on the practice.
Neighbours around Kensington Palace, which is home to Prince William and the Duchess of Cambridge, have complained to the council about the prospect of two years of disruption.
The site of the work is located 200 yards from Kensington Palace Gardens. Residents of the street include Chelsea owner Roman Abramovich and I’m A Celebrity winner Georgia Toffollo.
According to the Express, Kensington and Chelsea Council deemed the excavation as of “economic benefit” to the nation.
Prince William and Kate announced they would be extending their property in March last year.
The proposal application for the work read: “The addition of a basement story is required to allow for the accommodation of administration which must necessarily be moved out of rooms leased from the Royal Household in Kensington Palace.”
Local resident Donald Cameron argued there will be 20 trucks a day coming and going.
Another resident, Patrick Hope-Falkner, said: “Is everyone cowed by the involvement of a royal palace? No one is above the law.”
Hope-Falkner claimed it would be a “traumatic development to a listed building and a blatant defiance of the two-storey rule” to allow the extension.
Kensington Palace and Historic Royal Palaces declined to comment.