The neighbors, all of them quite well off financially, argued to the city council that the home extension will block the light and add noise and disturbances, the Daily Mail reported.
Pippa and James live in a reported $20 million, five-story home on one of London's most exclusive roads. The home boasts a gym, an underground cinema, an elevator, a "staff room" and six bedrooms.
The extension will add a new bathroom and separate male and female dressing rooms.
"We have reviewed the proposed plan, and strongly object to the suggested rear extension," Pippa's next-door neighbor told the city council. "It will completely block the sunlight which currently comes into our kitchen for a limited time in the middle of the day, and generally block the daylight into our kitchen from the adjacent window."
The neighbor added, "If the project goes ahead we will see significant morning light and sun loss in; our cherished outside patio, our main kitchen dining area which is designed as an orangery, our main office. The house should be big enough to be able to accommodate our neighbors' architectural plans within the existing structure."
Another well-heeled neighbor argued that Pippa's home was already renovated before her husband bought it in 2014, and he said that was a nightmare.
"My family lived through the [previous] extensive several years development a few years ago. It was a highly disruptive construction project with all the obvious inconveniences that a refurbishment of that size involves, he said. "At one stage it caused the tallest part and substantial part of the rest of garden wall to collapse into our garden, which could literally have killed persons though strangely we received no apologies from the then owner and we had to pay for all the damages done to our garden. The current application appears to be yet another floor on top of the extended kitchen, which will reduce both the view of vegetation from our property as well as the light."
Another neighbor said, "The completed extension would constrain the view over the gardens from the master bedroom, kitchen and staircase windows. The construction itself would cause considerable inconvenience to us and our children."
The arguments may very well fall on deaf ears, as the couple was already granted permission for the extension.