https://www.bbc.com/news/uk-58943184
The 25-year-old is being held under the Terrorism Act and officers have until Friday to question him.
The BBC understands Mr Ali was referred to the counter-terrorist Prevent scheme some years ago, but was never a formal subject of interest to MI5.
Whitehall officials told the BBC that the man being held was Ali Harbi Ali, a British man of Somali heritage.
Police said a man, who was held on suspicion of the MP's murder in Essex on Friday, was now being held at London police station after being rearrested under the Terrorism Act.
We may never know the motive...