The men were arrested in 2011 while attempting to smuggle the drugs into Egypt by the sea, close to Marsa Alam on the southeast coast. The Pakistani man was not detained.
Egypt's grand mufti -- the country's highest religious authority -- sentenced the men to death by hanging Monday, Ahram Online reported.
The court also ordered the men to pay a fine of $12.2 million.
The British government condemned the British citizen's sentence and said it would work to stop the execution, Ahram Online reported.
"The British government is extremely concerned at the death sentence passed down on a British national by an Egyptian court on 3 June," a senior press officer at the British Embassy in Cairo said in an email statement.
"Our consular team in Cairo are in contact with the British national involved and we will do our utmost to prevent this execution," the statement said.