Richard Dart, 29, who changed his name to Salahuddin al-Britani after converting, was said to have been one of three people detained in Ealing, west London, yesterday morning. He was arrested in the street.
The others detained in Ealing were a 21-year-old man and a 30-year-old woman held at separate home addresses.
Dart appeared in a BBC Three documentary, My Brother The Islamist, made by his stepbrother Robb Leech last year, which told how Dart, originally from Weymouth, Dorset, had been converted by controversial cleric Anjem Choudary.
In the documentary he spoke of his support for jihad and sharia law.
Meanwhile, in Stratford, east London, the home of the Olympics, three men believed to be members of the same Bangladeshi family were arrested in a raid on their home.
One, aged 24, was Tasered during his arrest but did not require hospital treatment, a Metropolitan Police spokesman said. The others were aged 18 and 26.
The group had been under MI5 surveillance for several months and, according to The Times, the location of the house - close to the Olympic Park - encouraged the security forces to act.
Neighbours said the occupants had been at the house for many years 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.
One local, who asked not to be named, described the men as "good people".
"They are religious and they go to the mosque," she said. "They are usual Muslim young boys."
Trainee taxi driver Stephen Maguire, 23, said he heard the police raid 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."
WATCH: Scroll down to watch My Brother The Islamist
The six, who include a former police community support officer, were being held at a south east London police station on suspicion of the commission, preparation or instigation of acts of terrorism.
Some of those held are understood to be British nationals.
The alleged plan involved Islamist extremists with potential targets in the UK, but was not linked to the Olympics, it is understood.
The London raids came on the same day that West Midlands Police closed the M6 toll road after smoke was seen emerging from a passenger's bag on a bus. The incident turned out not to be a terror threat; the smoke transpired to be the product of an electric cigarette.
Thursday's 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.
A spokeswoman for Scotland Yard said: "One of the men arrested by the Counter Terror Command 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, 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 is real and remains with us today."
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, based at MI5's headquarters at Thames House in central London, but is independent of the service.
Following the arrests, Choudary said that "there have been so many raids now because the Olympics is approaching".
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