Ardley Against Incineration applied to the High Court to have the decision overturned, but the application was refused in July and its last right of appeal has now also been rejected.
Jon O’Neill, chair of the campaign group, said: "Thanks to all who have supported is and given up their hard earned money over the last four years in fighting this case.
"We are obviously disappointed, and we just hope that the findings of the planning inspector and the secretary of state, upheld by the judges, are borne out in the fullness of time."
The proposed incinerator is expected to burn 300,000 tonnes of waste a year, generating enough electricity to power 38,000 houses.
Robert Ryan, head of projects at Viridor, said: "We were confident that our proposal for Oxfordshire was carefully and thoroughly developed and today’s decision reaffirms that.
"We can now start preparing for construction works to start so we can deliver a state of the art facility for Oxfordshire in 2014."