"I feel and understand that fear, and as the police officer-in-charge of preventing such an attack I know you want me to reassure you. I am afraid I cannot do that entirely. Our threat level has been at 'severe' for two years. It remains there.It means an attack is highly likely - you could say it is a case of when, not if," Sir Bernard Hogan-Howe, the chief of Metropolitan Police said.
"There's four or five cases where there is a sense of a plot, where they are planning and plotting and intending to commit an act of terrorism rather than just being extremists," the source told the newspaper.
Last week Ben Wallace, the UK's new security minister, held talks with retail bosses and operators of sporting venues to review security at stadiums and shopping centres.
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Another intelligence source said that Islamic State (ISIS) terrorists were increasingly going after "softer targets", as well as seeking to recruit people with mental health problems.
"Unbalanced people, mentally ill people, people with particularly violent or anti-societal or sociopathic tendencies are being recruited as foot soldiers; and then that is playing itself out in the most innocent and unassuming targets, such as the street crowds on Bastille Day in Nice," the source said.
The review, which started in March when Theresa May was home secretary and is now being overseen by her successor Amber Rudd, is expected to report in October.