The Foreign Office said it would "consider how to support any application for judicial review or clemency" that Lindsay Sandiford makes after she lost her appeal against a death sentence for drug trafficking.
A Foreign and Commonwealth Office spokesman said: "We are aware that Lindsay Sandiford's appeal to the Indonesian Supreme Court has been denied.
"We will continue to provide consular assistance to Lindsay Sandiford and her family at this difficult time."
Human rights organisation Reprieve has previously said it believes there is evidence to show that Sandiford was threatened and coerced into acting as a courier.
Indonesia has an estimated 114 prisoners on death row. Most of the more than 40 foreigners among them have been convicted of drug crimes, according to a March 2012 report by Australia's Lowy Institute for International Policy.
Five foreigners have been executed since 1998, all for drug crimes, according to the institute. There have been no executions in the country since 2008, when 10 people were put to death.