The four were part of a group of nine people, all members of the same family, who were detained in Turkey at the beginning of the month.
One of the nine, a 21-year-old man named in the media as Waheed Ahmed, the son of a British local politician, was arrested when he returned to Britain on Tuesday.
They were arrested on suspicion of the commission, preparation or instigation of acts of terrorism, police said.
Thousands of foreigners have joined the ranks of Islamic State and other militant groups in Syria and Iraq, many of them crossing via Turkey.
Turkish and other security services estimate some 600 are Britons, including Mohammed Emwazi, named “Jihadi John” in the British media, who has appeared in several Islamic State beheading videos.
About half of the 600 are thought to have returned home. -Reuters