Prime ministers have always been terrorist targets, though Downing Street is now well protected by fortified gates and armed police officers.
Naa'imur Rahman, of north London, has been charged with preparing to commit acts of terrorism.
Earlier this week a spokesperson for Ms May said British authorities had foiled nine terrorist plots in the last 12 months.
However, the Metropolitan Police released a statement earlier today confirming two men were arrested in the United Kingdom last week charged with preparing terrorist attacks. He said he was of no fixed abode and said his nationality was "Bangladeshi British".
Two men have been arrested on suspicion of plotting to kill the Prime Minister by using a bomb disguised as a bag to blow off the gates of Downing Street and then attack her with knives, The Independent.
In a related allegation, Imran is accused of trying to obtain a fake passport in order to leave the United Kingdom and travel to Libya.
When speaking to cabinet members, Parker noted that the Islamic State group had faced defeats. Imran said he was "Pakistani British".
Both men are in police custody and will appear before Westminster Magistrates Court on Wednesday. Nobody was injured during that attack.
Mr Parker's Cabinet briefing came on the same day that a review of a string of United Kingdom terror attacks earlier this year revealed that the Manchester Arena bomber was known to MI5 and his attack, in which 22 people died, could have been stopped "had the cards fallen differently".
The police said there were now 500 counter-terrorism investigations involving 3,000 people and more than 20,000 other people have been investigated in the past.
The men were arrested in raids by Scotland Yard's counterterrorism command in London and Birmingham on November 28.
Parker spoke to members of Theresa May's cabinet about terrorist threats.