The 44-year-old former Take That star - who is married to actress Ayda Field - is hoping to have a new pool constructed in his West London home, but Jimmy has strongly opposed the move over the last four years, arguing it would be ''catastrophic'' for his own property.
However, Kensington and Chelsea Council's planning committee has deferred a decision, meaning the battle is set to rumble on.
The row between two of the UK's most high-profile musicians was sparked shortly after Robbie bought the house from film director Michael Winner.
Jimmy, 74, has lived in his current home since 1972 and has opposed Robbie's plans because he fears the vibrations caused by the construction work could lead to irreversible damage.
The former Led Zepplin star previously detailed his concerns in a two-page letter to the council, telling the local authority that his home is ''one of the most historic buildings in the borough''.
He explained: ''Having protected the Tower House for over 40 years, I am now continuing the fight against a new threat to this precious and unique building.''
Jimmy has also attended a council planning meeting where the controversial application was discussed.
He told the councillors: ''I feel it is my duty to protect that house, I really do.''
Robbie's plans - which he submitted to the local council in January - include designs for a swimming pool and a gym facility to be constructed underneath his London house.
Kensington and Chelsea Council have now decided to defer the decision and although the issue remains unresolved, Jimmy has insisted he's ''very pleased'' with the outcome.
He said: ''I think the deferment was a very good conclusion.''
American Thighs was released on this day in 1994.