Andargachew Tsige was sentenced to death in 2009 in absentia and another trial handed him life behind bars three years later. He was arrested in Yemen earlier this year and extradited to Ethiopia.
On Monday, Britain summoned one of Ethiopia's top diplomats in London to meet Foreign Office minister Mark Simmonds, who expressed "deep concern" that Andargachew had not been granted access to the British consulate.
"Mr Simmonds asked the chargé to urge his government to deliver on previous commitments to provide consular access without further delay, and to provide assurances that they do not intend to carry out the death penalty imposed in absentia," a statement from the Foreign Office said.
Andargachew, secretary-general of the Ginbot 7 group, was among 20 opposition figures and journalists charged with conspiring with rebels, plotting attacks and attempting to topple the government.