Three men accused of travelling to Pakistan for terrorism training, including a British Muslim convert, appeared in court today.
A woman alleged to have been in possession of terrorist material also attended the hearing at Westminster Magistrates' Court in London.
One of the suspects lives in Stratford, east London, where the Olympics is being held, but Scotland Yard has said none of the alleged offences was linked to the Games.
Richard Dart, of Broadway, Ealing, who appeared in a BBC Three documentary after converting to Islam, is charged with preparing for acts of terrorism between July 2010 and July 2012, alongside Imran Mahmood and Jahangir Alom.
As well as the terrorism training allegation, they are accused of travelling abroad to commit acts.
Dart, 29, Mahmood, 21, from Dabbs Hill Lane, Northolt, west London and Alom, 26 of Abbey Road, Stratford were arrested between July 5 and 7, alongside the woman, Ruksana Begum.
Begum, 22, of Provost Estate, Islington, north London, is charged with possession of a digital memory card containing a document likely to be of use to a terrorist.
District Judge Howard riddle remanded all four in custody. They will appear at The Old Bailey on July 31.
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