Two men are suspected of conspiring to attack Downing Street armed with an improvised bomb, suicide vest and knives.
News reports have claimed that MI5 has thwarted nine terrorist plots in the last 12 months.
Rahman appeared with a co-defendant, 21-year-old Mohammed Imran, from Birmingham, who is also charged with preparing to commit acts of terrorism.
London based Naa'imur Zakariyah Rahman, 20, who described himself in court as Pakistani British, was arrested last week and charged on Tuesday. When asked about his nationality in court, Imran said he was Bangladeshi British.
The UK security authorities believe that they have foiled a possible plot to assassinate Prime Minister Theresa May, where the killers had planned to bomb their way into Downing Street, the PM official residence.
Both men were arrested by officers from the Met's Counter Terrorism Command in raids in London and Birmingham on Tuesday November 28. The recording would have given Imran greater credibility with the terrorist organization, the document said.
Chief Magistrate Emma Arbuthnot remanded them in custody to appear at the Old Bailey on December 20. Anderson said the Manchester bombing attack, which killed 22 people at a music concert in May, could have been stopped "had the cards fallen differently".
The Prime Minister's official spokesman declined to discuss the details of the foiled attacks.
"Cabinet ministers heard that while Daesh suffered major defeats in Iraq and Syria, this did not mean the threat is over".
Terror attacks at Westminster, London Bridge, Finsbury Park, and in Manchester this year killed more than 30 people and injured hundreds more.