The Led Zeppelin rocker, 72, lives in a 19th Century property in the West Kensington area of the British capital, where fellow musician Robbie also has his home.
And when the Angels singer submitted plans to local planning chiefs for permission to modernise his $28 million (£17.5 million) mansion with a new extension Jimmy objected, penning a number of letters to council officials claiming the building work could damage his historic home.
Robbie has already withdrawn two sets of plans, and has subsequently submitted a third planning proposal to Kensington and Chelsea council officials for approval.
The rock veteran has now applied to carry out his own renovations by submitting his own building plans for approval by council officials via building design company Andrew Townsend Architects.
According to Britain's Daily Mail newspaper, the application outlining legendary guitarist's building plans claims they are necessary to preserve his property, which is listed by the British government as historically and architecturally significant.
"Decay is taking place to high-level brickwork, terracotta and stone masonry and the proposed works are designed to address these problems," the proposal reads. "The works on the second floor will almost certainly need scaffolding to be erected around the house."
A spokesperson to Robbie refused to disclose to the paper if the former Take That star would lodge any objections to his neighbour's plans.
However one bemused local told the British newspaper: "Jimmy's got some cheek after all the fuss he made about Robbie's plans, he's bringing in the builders himself."
Decisions on whether Robbie and Jimmy's planning applications will be successful are due to be made later this month (Jul16).
Jimmy's home's historic status is due to it being designed by eminent Victorian architect William Burges, as well as having been home to British poet John Betjeman and Irish actor Richard Harris.
Both parties planning proposals are set to be considered by council officials later this month (Jul16).