It said the aircraft was on its way to Juba, the capital of South Sudan, to collect any UK nationals who wanted to leave.
A spokesman said about 150 Britons from an estimated 500 in Juba had so far expressed an interest in leaving and those who remained were advised to stay at home and avoid travel.
Britain has also withdrawn all non-essential embassy staff, while keeping its mission in Juba open. It advises against all travel to the South Sudanese capital.
Government forces were battling rebels to keep a foothold in a flashpoint town yesterday, in a conflict that may split South Sudan along ethnic lines and has prompted an east African bid to mediate. South Sudanese president Salva Kiir held talks in Juba yesterday with African mediators seeking to end the conflict.
A ruling party official said the president's earlier claim that an attempted coup had triggered the fighting was false. Instead, the violence erupted on Sunday when the presidential guard attempted to disarm fellow guard members in the Nuer tribe, said Choul Laam, of the ruling Sudan People's Liberation Movement.
Those who tried to do the disarming were members of the majority Dinka tribe of Mr Kiir, Mr Laam said.