He is accused of plotting to kill Prime Minister Theresa May by planting an improvised bomb at the entrance to Downing Street.
Another report by Sky News said that the plot was allegedly planned by an Islamist extremist.
A man died in a terrorist incident at Finsbury Park mosque in north London in the same month - and, in September, an attempt to bomb a Tube train at Parsons Green station failed.
Read alsoSBU: Female suspect in assassination of counterintel colonel in Mariupol detained in OdesaAfter reviewing the security services' actions in relation to four terrorist attacks in the United Kingdom this year, Mr. Anderson said: "It is conceivable that the Manchester attack, in particular, might have been averted had the cards fallen differently".
"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.
The 27-year-old had been watched by MI5. He is accused of preparing acts of terrorism.
Naa'imur Zakariyah Rahman is accused of planning an explosion outside May's Downing Street office then trying to enter the building with a suicide vest and a knife in a bid to kill her.
When speaking to cabinet members, Parker noted that the Islamic State group had faced defeats. "Rather it is spreading to new areas, including trying to encourage attacks in the United Kingdom and elsewhere via propaganda on social media".
A review of recent attacks by British security service is due to be released soon.
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".
His report also noted that the Pakistani-origin ringleader, Khuram Butt, of the terrorist attack on London Bridge in June had been on the security services' radar for two years.
Jamie Dettmer reported this story for VOA News.
However, Anderson noted that most terror plots continue to be prevented before they can be carried out. Mario Ritter adapted it for VOA Learning English.