The alleged plan involved Islamist extremists with potential targets in the UK, but was not linked to the Olympics, it is understood.
The arrests were part of a pre-planned intelligence-led operation by the Metropolitan Police counter-terror command along with armed officers, but the threat was not thought to be imminent.
Five men and a woman were arrested on suspicion of the commission, preparation or instigation of acts of terrorism and were being held at a south-east London police station, police said.
Three of the men, believed to be members of the same Bangladeshi family, were arrested in a raid on a house in Stratford, east London.
One, aged 24, was Tasered during his arrest but did not require hospital treatment, the Met spokesman added.
The others were aged 18 and 26.
Neighbours said the occupants had been there for more than a year and there were frequently people coming and going from the property.
They spoke of seeing men in Muslim-style robes and a woman in a burka.
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."
In Ealing, west London, a 29-year-old man was arrested in the street, and a 21-year-old man and a 30-year-old woman were held at separate residential premises.
Some of those held are understood to be British nationals, and one is a former police community support officer.
A spokeswoman for Scotland Yard said: "One of the men arrested by the Counter Terror Command today served as a PCSO for the MPS from May 2007 to September 2009 when he resigned.
"He was not deployed in any specialist or sensitive roles."
The force said that eight residential premises in east, west and north London and one business premises in east London were being searched.
The arrests come after Jonathan Evans, the director-general of the Security Service, warned last month that Britain had experienced a "credible terrorist attack plot about once a year since 9/11".
"In back rooms and in cars and on the streets of this country there is no shortage of individuals talking about wanting to mount terrorist attacks here," he added.
The threat to the UK from international terrorism is currently rated substantial - the third highest of five levels.
The rating is set by the Joint Terrorism Analysis Centre (Jtac), based at MI5's headquarters at Thames House in central London, but is independent of the service.
:: Meanwhile, Lancashire police have charged a 20-year-old man from Burnley with six terrorism offences following his arrest in another pre-planned operation.
Niall Florence was arrested at his home during the operation on December 9 last year. He has been released on bail until July 20.