The extremist Islamist plot involved a bomb attack on Downing Street, the prime minister's residence, and an attempt to kill May in the ensuing chaos, Sky reported.
The terror attack was foiled after a joint operation by Scotland Yard, West Midlands Police, and MI5. Parker reportedly told Cabinet ministers that British authorities have broken up nine potential terrorist attacks this year.
Two people are arrested - 20 and 21 years old, who are already accused of preparing a terrorist act.
10 Downing Street is the location of the prime minister's office.
Sky's Crime Correspondent Martin Brunt said: "I understand that the head of MI5, Andrew Parker, briefed Cabinet ministers today, such is the seriousness of what they believed they have uncovered". According to the report undertaken by David Anderson, British security forces had missed opportunities to thwart the Manchester attack.
The plan, revealed to the British Cabinet on Tuesday, allegedly involved planting a bomb outside the entrance to Downing Street gates before attackers would stab the United Kingdom leader in the ensuing chaos.
Rahman is charged with assisting Imran in "making preparations for the attack", according to the FT.
Security measures were introduced in the 1970s but were increased in the 1980s as the threat from Irish republican groups grew.
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