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The High Court will be asked to decide whether to uphold a control order used by the Home Secretary to ban a terror suspect from the capital.
The man, referred to only as CD, was removed after security services named him as the leading figure in "a close group of Islamic extremists based in north London".
Mayor Boris Johnson has appealed to Government ministers to keep him away from the capital.
He said of CD: "It's clear from the court papers that he rejects and would like to destroy everything that makes this a great city. We don't want this man in London."
MI5 reports said CD had trained alongside the men behind the 21/7 bomb plot and attempted to obtain firearms.
Theresa May used the control order last February to relocate him to a Midlands city to stop him meeting his associates in the capital.
At a recent High Court hearing, the Home Secretary was ordered to contribute to the cost of visits by family members who remain living in London.
But the relocation powers are being ditched by the Coalition under new terrorist prevention and investigation measures (TPIMs).
The hearing before Mr Justice Owen is to determine whether the current control order can properly be upheld.
The court will also have to decide whether or not the order is having a "disproportionate" impact on the father of two, who has joint UK-Nigerian nationality.
