It is unclear when Waste4Fuel's High Court hearing, adjourned on May 8, will reconvene.
The hearing, which had been expected to last three days, began at the Royal Courts of Justice on May 6.
Although it was due to start again in June, the Environment Agency (EA) today confirmed no date has been set.
The EA is seeking contempt charges against Waste4Fuel, former company director Bryan Hughes, new company director Shelley Hurst and site manager Jonathan Beckson.
This comes after it had acquired a High Court order in November last year, requiring all combustible waste to be removed from the site in Cornwall Drive, St Paul's Cray, by May 1.
Fire services have been called to the plant numerous times in the last year and a half, with locals voicing concerns about the health implications of fumes being emitted.