The Waste4Fuel High Court hearing, which started this week at the Royal Courts of Justice, has been adjourned until at least June.
The Environment Agency (EA)'s case against Waste4Fuel, whose site in Cornwall Drive, St Paul's Cray, has caused misery for local residents, began on Tuesday afternoon.
The hearing was expected to last three days.
The EA is seeking contempt charges against Waste4Fuel, former company director Bryan Hughes, new company director Shelley Hurst and site manager Jonathan Beckson.
A High Court order was acquired in November last year, requiring all combustible waste to be removed from the site by May 1.
Fire services have been called to the plant 12 times in the last 12 months, with locals voicing concerns about the health implications of fumes being emitted.
Jon Griffin, waste team leader at the Environment Agency, said: "As far as we are concerned, the site should operate in accordance with the final terms of the court order issued last November, meaning we expect the site operators to remove combustible waste from the site.
"Between now and the next appearance at the High Court, our officers will continue to monitor Waste4Fuel’s compliance with the original court order closely."