The Metropolitan Police had said they pulled a woman from the water after MP Stephen Gilbert claimed he rescued her:
"At 1950 the marine policing unit responded to reports of a woman in the River Thames near Westminster Bridge. They recovered her from the water and took her to hospital. Next of kin have been informed," the force said in a statement.
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A woman hit by police gunfire during a counter-terrorism operation has been arrested after being released from hospital.
Police have been granted extra time to question a man who is being held on suspicion of planning a terror attack.
The man opened fire at the house, shattering the front door and window.