Jamila Henry, 21, was stopped by officers in Ankara earlier this week and deported to the UK and arrested here today on suspicion of preparing acts of terrorism.
Henry handed over her twin sister Jalila Henry's documents to officers when she was arrested, apparently heading for the Syrian border.
The passport switch caused confusion among Turkish intelligence services who released Jalila's name to local media after apprehending her at a bus stop on Monday.
Friends said the twins had gone in "totally different directions" since leaving school in south-west London.
More From This Section
Jalila is pictured on her Facebook page drinking and smoking.
Jamila, meanwhile, wears a traditional headscarf and is said to spend her spare time studying the Quran after converting to Islam in her teens.
The twins' mother Patricia Henry, 50, said she was "getting together with relatives" to discuss the situation.
Scotland Yard confirmed that Jamila Henry was being held in police custody after being arrested at by counter- terror officers at Luton Airport near London.