Naa'imur Zakariyah Rahman, 20, has been remanded in custody at Westminster Magistrates' Court over the reported plan for a knife and bomb attack at the Prime Minister's home.
A 20-year-old man appeared in court on Wednesday accused of plotting to kill British Prime Minister Theresa May.
Parker told ministers that United Kingdom authorities had broken up nine potential terrorist attacks over the past year.
Also accused is 21-year-old Mohammed Aqib Imran, who was arrested in Birmingham. When asked about his nationality in court, Imran said he was Bangladeshi British.
It's alleged two would-be terrorists planned on launching an "improvised explosive device at Downing Street" before locating the Prime Minister and killing her, Sky News has reported.
"The secondary attack was to be carried out with a suicide vest, pepper spray and a knife", he told the court.More news: Facebook unveils messaging App for kids
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Imran was accused of trying to join Daesh in Libya, the prosecutor alleged. Imran said he was "Pakistani British". Opportunities to stop the most fatal of those - a suicide bomb attack at an Ariana Grande concert in Manchester in May - were missed, according to the report by senior barrister David Anderson published Tuesday.
"The UK is facing an intense threat from terrorism, one which is multi-dimensional, evolving rapidly and operating at a scale and pace we have not seen before", London's Metropolitan Police said on Tuesday.
Downing Street is protected by armed police officers and separated from the public by fortified gates.
The alleged plot highlights the extreme threat still faced by the United Kingdom in a year blighted by terrorist atrocities which claimed 36 lives.
After the meeting, the prime minister's spokesman said: "The prime minister led thanks to the tireless work of staff at MI5 to combat the unprecedented terrorist threat".