It was not immediately known what charges would be brought against the suspects detained on Wednesday, said defence lawyer Selahattin Karahan.
The state security court freed 15 others who were being held in the probe.
On Tuesday, nine people were charged with belonging to or aiding and abetting an illegal organisation in the investigation into the bombings at the British consulate and the Istanbul offices of London-based banking giant HSBC.
Eight people have also been charged with involvement in the bombings of two Istanbul synagogues five days earlier. Officials said several more were in police custody.
Turkish Prime Minister Tayyip Erdogan accused Britain of not sharing intelligence about possible future attacks with Turkish authorities after London said on Tuesday that "further attacks may be imminent" in Istanbul and the capital Ankara.
Australia issued a similar alert on Wednesday.
“If there is a common platform against international terrorism, this information must be given to the concerned country. If the source for this kind of information is sound... it should not be given to the media," said Erdogan.
Turkish authorities say London is
not sharing intelligence
“There is a watering down of intelligence here," he said.
But a British Foreign Office spokeswoman said London conveyed information to countries where a threat occurred to reduce the risk of an attack.
Groups linked to al-Qaida network claimed responsibility for the 20 November attacks on the British targets, as well as similar coordinated bombings at two synagogues in which 25 people died the previous week.
Police in Istanbul, a city of more than 10 million people, conducted spot checks on vehicles crossing a suspension bridge connecting the Asian half of the city with Europe.
An armoured police vehicle sat outside Istanbul's international airport, and security personnel searched some bags before allowing passengers to enter terminals.