His oral application follows an Appeals Court refusal of his written application for leave to appeal.
A spokesperson for the Mayor said: The High Court's decision means that WLWA could tender for a waste contract to incinerate West Londons waste.
The effect of such a decision is that 36 per cent of London's rubbish will be sent to incineration.
In response WLWA general manager Mike Nicholls said: Restricted landfill allowances mean that WLWA urgently needs to divert its waste from landfill.
"[We have wanted] to invite tenders from all technologies to do this [but] no decision has been taken on which technologies can be used. The Mayor wants to stop the possibility of a tender being received from the Lakeside incinerator, being built 200 metres over the WLWA boundary.
Nicholls challenged the Mayors figures and added: In the unlikely event that the tendering outcome was for maximum contract tonnage to be incinerated, this would still only represent 4% of Londons waste not 36% as the Mayor said.