Four other people; two men, aged 20 and 16, and a woman, 20, have been arrested in the operation conducted by Scotland Yard, BBC reports.
The arrestees have been placed in custody at South London police station. The woman shot in the operation has been whisked to hospital, placed under police surveillance.
She is in serious but stable condition, police told BBC.
The operation took place a day after a man aged 27 armed with knives was arrested in Westminster, near the Parliament. The man was reportedly carrying two knives.
Armed police pinned down the man after receiving tips-off from a man from the Muslim community who claimed to know the terror suspect. MI5 forces and police then began tracking the man.
Police initially treated the case as a terror plot but gave up after realizing that the man had severe mental problems, The Guardian reports.
Police ruled out link between the Thursday and the Wednesday operations.
The British capital has been further on the alert since March 22 after a Daech militant known as Khalid Masood on board a 4-wheel car crashed pedestrians on Westminster Bridge and the parliamentary estate five weeks ago.
After he hopped from the car, he stabbed a police officer to death. Three people died from the car attack. Police shot Masood dead.