Abu Rumaysah, born Siddhartha Dhar, was arrested by Scotland Yard as a terror suspect in September and was released on bail.
But according to BBC London he left London on a bus bound for mainland Europe and is now living under the Islamic State.
The Metropolitan Police's counter-terrorism command says it is working to establish where he is.
Rumaysah, 31, was arrested on suspicion of encouraging terrorism on September 25 as part of an investigation into the banned extremist group al-Muhajiroun.
He has close links to radical preacher Anjem Choudhary, who was head of al-Muhajiroun.
The two men were arrested along with eight others.
But days later Rumaysah is believed to have boarded a bus from Victoria Station in London for Paris, from where he is believed to have travelled on to Syria.
Rumaysah, a father of four, has publicly expressed his views was on the BBC's Sunday Morning Live programme, before he was arrested.
Then he said: "Now that we have this Caliphate (Islamic state) I think you'll see many Muslims globally seeing it as an opportunity for the Quran to be realised."
Met Police Commissioner Sir Bernard Hogan-Howe has said that an estimated 500 British people are fighting for IS in Syria and Iraq.
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