One of the six, who are aged between 18 and 30, was Tasered by police. Eight homes in west, east and north London and one business have been searched.
It is understood the arrests relate to a possible plot involving Islamist extremists, with potential UK targets.
Three of those held are brothers - one an ex-police community support officer.
He served with the Metropolitan Police for more than two years before resigning in September 2009.
The force said he had not been "deployed in any specialist or sensitive roles".
The brothers, aged 18, 24 and 26, were detained in Abbey Road, in Stratford, east London, during an operation involving armed officers.
The BBC understands they are Jahangir, Mohammed and Moybur Alom.
Richard Dart, a Muslim convert who uses the name Salahuddin al Britani, was also detained in the raids, it is understood. He features in a YouTube video which criticises the Royal Family and British military action in Muslim countries.
The Metropolitan Police said the arrests were not linked to the Olympics or Paralympic Games.
It is understood that police involved in the long-running operation decided to act on Thursday on the grounds of public safety.
The UK  
          terrorism threat level
 is unchanged from "substantial", which means a terrorist attack is a "strong possibility". There are two higher levels - "severe", meaning an attack is "highly likely", and "critical", meaning an attack is "expected imminently".
Some - if not all - of those arrested on suspicion of the commission, preparation or instigation of acts of terrorism are British nationals, BBC home affairs correspondent Danny Shaw says.
They include a 21-year-old man and a 30-year-old woman, who were detained at separate addresses in Ealing, west London, while a 29-year-old man was arrested in an Ealing street. The woman is married to one of the men.
All six have been taken to a police station in south-east London.
The 24-year-old man who was Tasered during his arrest in Stratford did not need hospital treatment, police said.
An eyewitness to the Stratford raid, Mark Window, told the BBC he had been woken up by an explosion at 04:15 BST.
"I looked out my window, saw loads of mini-explosions going off still, loads of black-clad figures milling around," he said.
"One was halfway up a ladder, through a window, and you realise it's some sort of police operation going on instead of kids messing about with fireworks which is what you think when you first wake up."
Trainee taxi driver Stephen Maguire, 23, said he heard the police from his bedroom in Eastbourne Road, which overlooks the front of the house.
"I heard the biggest bang ever and I saw a massive cloud of smoke and torches going up at the windows," he said. "It sounded like they were gunshots but they weren't."

The 21-year-old beat Thailand's Tawin Hanprab 6-4 in the final.
Luisito Pie of the Dominican Republic and South Korea's Kim Tae-hun won the bronze medals.
Kim So-hui won gold in the women's -49kg final. The South Korean defeated Tijana Bogdanovic of Serbia 7-6 in a thrilling contest.
Patimat Abakarova of Azerbaijan and Thailand's Panipak Wongpattanakit took the bronze medals.
Five men and a woman suspected of terrorism offences have been arrested in London as part of an intelligence-led investigation involving MI5.
[NEXT_CONCEPT]
Zhao Shuai won China's 19th gold medal of the Rio Games by taking the men's -58kg Olympic taekwondo title on Wednesday.