Khalid Mohammed Omar Ali, 27, was arrested on 27 April near Parliament Square in Whitehall.
In an unrelated incident, six people were arrested following evening raids in Willesden and Kent, including 21-year-old Mohamed Amoudi.
The maximum terror suspects can be held for with judicial approval is 14 days.
Police have been given authorisation by a court to detain all the suspects for several more days.
Mr Ali was found carrying knives near the Houses of Parliament and was detained by armed police.
He is a British national who is believed to have gone to school in Tottenham, north London, but was not born in the UK.
The Metropolitan Police said he had been detained on suspicion of terrorism offences.
He had been on the force's radar for some time and it is thought police acted after a concerned family member contacted them.
It also emerged on Saturday that he had spent time in Afghanistan, returning to the UK at the end of last year.
The second operation took place at a house in Harlesden Road, which had been under observation by police.
It was revealed on Saturday that Mr Amoudi had previously been quizzed by British authorities under suspicion of trying to travel to Syria to join so-called Islamic State
He was arrested alongside a 20-year-old woman, a 16-year-old boy, and a man and woman both aged 28, as well as a 43-year-old woman, who was arrested at another raid in Kent.
All of them were detained on suspicion of the commission, preparation and instigation of terrorist acts.
A 21-year-old woman was also shot during the raid and remains in hospital. She is likely to be questioned when she is well enough to be discharged.
The Met said the two incidents were unrelated.
Neil Basu, deputy assistant commissioner, said that in both cases he believed the force "contained the threats that they pose".
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Detectives have been granted more time to question seven suspects detained in two separate counter-terrorism operations in London on Thursday.