Despite the concerns of residents that the incinerator poses a health hazard, the Labour Welsh Government have still not decided if an Environmental Impact Assessment should be made.
Earlier the Vale Conservative council group forced the Vale Council to hold an independent inquiry.
Now local Conservatives are demanding the Welsh Government permanently stop the project with a legally binding Discontinuance Order.
Matt Smith said "The Council and Welsh Government need to stop taking Barry for granted and put an end to this polluting powerplant for good".