Cuadrilla Resources has endured more than two weeks of protests near the town of Balcombe near the southeastern coast. The company is engaged in preliminary oil exploration there and environmental groups worry it's a prelude to a broader campaign using hydraulic fracturing, known also as fracking.
The drilling technique has led to an oil and natural gas boom from shale deposits, notably in the United States.
Greenpeace said it wanted to have a debate about fracking with Cuadrilla online through the social networking site Twitter.
"We asked fracking company Cuadrilla, currently being surrounded by protesters in the Sussex village of Balcombe, for an open, transparent debate on Twitter about, well, fracking," it said Wednesday. "Sadly, we were rebuffed."
The company said it would need another drilling permit for fracking operations in Balcombe. Cuadrilla told the BBC this week it was "unlikely" the site would become a full production site.
British Prime Minister David Cameron wrote Monday in The Daily Telegraph the country would "miss a massive opportunity" to stimulate the economy if it turned its back on fracking.
Critics of fracking worry about groundwater contamination. Cameron said many of the environmental issues could be abated with proper oversight.