Naa'imur Zakariyah Rahman, 20, has been charged with preparing acts of terrorism and was remanded in custody during a hearing at Westminster Magistrates' Court.
The 20-year-old appeared alongside Mohammed Aqib Imran, 21, who is accused of trying to join Islamic State and preparing acts of terror.
Rahman, of Ballards Lane, in Finchley, north London, is also charged with assisting Imran in terror planning.
The pair, who were arrested in armed police raids in London and Birmingham last week, will appear at the Old Bailey on 20 December.
MI5 head Andrew Parker briefed Cabinet ministers with details of the alleged plot to assassinate the Prime Minister on Tuesday.