Lindsay Sandiford's lawyers still have the option open to ask the Court of Appeal to intervene in her case.
Aidan O'Neill QC told the court a competent lawyer had been found who was willing to waive fees and act pro bono, but required "operational costs", estimated at £2,500, to be met.
Dismissing Sandiford's case, Mrs Justice Gloster said: "We entirely understand the deep concerns of Mrs Sandiford and her family about Mrs Sandiford's predicament in Indonesia, but we must apply the law as we hold it to be."
Inside the Bali prison where British woman Lindsay Sandiford is being held after being sentenced to death for drug trafficking.
The Government said it strongly objects to the death penalty imposed today on a British woman who trafficked drugs into Indonesia.
The judge appears to have rejected any calls for leniency for Lindsay Sandiford. Execution is by firing squad in a jungle clearing.