"The action was pre-planned and intelligence led. There was no immediate threat to public safety," the West Midlands Counter Terrorism Unit said in a statement.
On April 4, a group of five men and one woman was arrested at the southern English port of Dover on the same charges.
Another arrest took place on April 1, when nine Britons were detained in Turkey after trying to illegally cross the Syrian border. The son of a Labour party councilor and his family were among the detainees.
Many would-be jihadists travel to war-torn Syria through the Turkish border to join various extremist groups, in particular the Islamic State (IS). The group's active propaganda on social media especially targets young people.
According the International Centre for the Study of Radicalization and Political Violence, about 600 British nationals have joined militant groups in Iraq and Syria.
