Hackney Council claims that a strictly Orthodox synagogue, built without planning permission in Stamford Hill, is "blocking the sunlight" of nearby families and says its extension must be demolished.
The synagogue, in Bethune Road, was served with an enforcement notice and given three months to demolish an extension and turn the building back into a family home.
The council alleges that notices have so far been "ignored" by the shul.
Yankel Grossberger of Satmar Limited is appealing against the enforcement notice on the extension and a public inquiry will be held at Hackney Town Hall on Tuesday.
The extension is more than three metres high and 10 metres long and stretches to the boundary of the garden, with four air conditioning units on top of the structure.
The synagogue maintains the extension has been in place for 10 years but the council disputes this. No planning application has ever been received for the extension. Concern has been expressed by Hackney that the use of the house as a synagogue means a loss of value housing for large Charedi families.
A council representative said: "The planning process is designed to try and reconcile the impact of new development on a neighbourhood. When a person ignores the process and brings forward an unauthorised development, it brings with it an adverse physical effect on a neighbourhood and erodes the quality of life experienced by a local community.
"It is important that development proposals are submitted to the planning authority before development commences. The council will take enforcement action against those who choose to ignore the planning process."