The Hollywood couple are seeking to move their kitchen, split their ground floor reception room into two, and replace the first floor rear window.
But locals have objected to the plans, the Telegraph reports, alleging it would not be in keeping with the Grade II Victorian terrace which is in a conservation area.
A planning agent representing the couple wrote in a submission to Camden Council: “The proposed new extension would replace an existing late 20th century conservatory which is poorly constructed, inefficient (it is very cold in the winter and it overheats in the summer), and out of keeping with the original building.
“The enlarged extension allows the kitchen (the busiest room in the house) to be relocated to the rear of the property giving it direct contact with the garden and much improved natural light.”
“Internally the spine wall between the ground floor reception rooms would be healed and the existing double doors from the entrance hall separated and re-hung as single doors into the respective reception rooms.
“So the most important rooms in the house would be reinstated to their original form.”
But Richard Simpson, acting for Camden Council's Primrose Hill Conservation Area Committee, lodged objections, raising concerns about replacing the first floor window as it would involve removing a type of glazing.
The committee, which advises the council on heritage issues in Primrose Hill, said the glazing was “a characteristic of the windows in houses of this date” in the local area.
A decision on the planning application is due to be made later this month.
The pair bought the property in 2008. They previously won a battle in 2017 to keep a 65ft tree behind the building, after a neighbour wanted to axe it.
Although some neighbours had wanted the tree axed, saying its roots were causing an issue, Camden Council later issued a tree protection order meaning it had to stay in place.
The Standard has contacted representatives of Craig and Weisz for comment.