In April, the energy secretary Alok Sharma granted a development consent order for the plans, which would nearly double the treatment capacity of Cory Energy's existing Riverside waste facility at Belvedere in the London Borough of Bexley, while also more than doubling its energy output.
Last week, Khan wrote to two local MPs, Jon Cruddas and Abena Oppong-Asare, who had campaigned against the proposals, explaining he had sought a judicial review of the minister's decision in May.
In June, the letter said, Khan was granted a full hearing to look at the approval, which will now be held at the High Court in October.
The letter said that Khan had written to Sharma in May, arguing that the approval "was made in haste, fails to address the adverse environmental effects of a new incinerator particularly on climate change, and takes us off course from achieving long-term sustainable waste management" - concerns which the letter said formed the basis of the judicial review bid.
Khan also said in his letter to Cruddas and Oppong-Asare: "Regarding the impact of the incinerator on the residents of Rainham Town Centre and neighbouring areas in particular, I agree that this was an important omission from the Environmental Impact Assessment of the project.
"We raised this repeatedly throughout the examination, but the inspector took no action to seek more information on this point. We are taking further legal advice on this matter."
Cruddas said news of the judicial review "is a real win for local people who have fought with me since the beginning, but the fight isn't over yet".
A Cory Energy representative said: "We are disappointed by the decision to allow the judicial review to proceed given the rigorous process carried out by the examining authority and the level of scrutiny from the secretary of state.
"London has a clear waste infrastructure capacity gap which urgently needs investment and energy recovery facilities like the Riverside Energy Park have a key role to play in the responsible treatment and disposal of the capital's non-recyclable waste."
A version of this story first appeared on ENDS Report.