Jonathan Hall, the Independent Reviewer of Terrorism Legislation, also warned former soldiers and police officers,who are used to covert work, “need to be worried”.
It comes amid fears the Kremlin is masterminding a hybrid warfare operation on British shores.
UK troops were scrambled to American air bases on Tuesday after drones were spotted flying overhead.
And many senior members of the Government were banned from travelling to Russia, as diplomatic relations plunged to a new low.
Mr Hall told LBC: “If you think about Russia, it doesn’t have a huge number of covert intelligence officers in the UK.
“I mean, many of them were expelled after the Skripal incident in 2018. I think 23 were expelled. So, the way in which the FSB and the GRU, the military intelligence of Russia, is going to operate, is going to operate through people like you and me. It’s going to pay private detectives.
“It could reach into an organised crime group and say to someone, look, we aren’t physically present in the UK, but we want someone to fly a drone, we want someone to insert something into a computer or carry out some act of sabotage.
“And it’s those individuals, those members of the public, who might be tempted by money, or perhaps by ideology, but most likely money, to help these foreign intelligence services.”
Mr Hall said former military personnel were amongst those who should be most concerned about being targeted by Russian intelligence officers.
He said: “I think the people who should most be on their guard are people who’ve got military training.
“So people who’ve left the military and left the police, who’ve got knowledge of how to carry out some sort of covert activity, who get approached by someone who they have suspicions about, because they, you know, they’re not stupid.
“I think those people need to be very, very careful indeed, because they have the capability that the sorts of people that the Russians could approach, and they need to be, I think they do need to be worried.
“I think the point of the law, anyway, is that it’s no longer good enough to say, well, I didn’t know for sure, but I’m going to take the money anyway.”
MI5 Director General Ken McCallum said Russia and Iran are on a mission to cause “mayhem” with an increase in arson, murder, kidnap and sabotage conspiracies.
The threat Moscow poses on Britain’s streets is “getting worse”, he warned.
Mr McCallum said Russia’s GRU intelligence agency, which was responsible for the Novichok poisonings in Salisbury in 2018, is behind the “sustained mission”, adding that Putin’s “henchmen” are ramping up arson and sabotage operations across Europe “in the misguided hope of weakening Western resolve”.
Britain’s top intelligence officer said Russia and Iran are hiring criminals to carry out their “dirty work” and acting with “increasing recklessness”.
At least 24 alleged saboteurs have been arrested so far this year after being recruited by Russian spy chiefs.
A wave of fires at arms factories and military-related industrial sites in the West has alarmed intelligence chiefs. Suspected plots have been detected in London, Germany, Czech Republic and Sweden.
Mr McCallum, speaking at the Counter Terrorism Operations Centre in west London on Tuesday, said: “In just the last year, the number of state threat investigations we’re running has shot up by 48%.
“The more eye-catching shift this year has been Russian state actors turning to proxies for their dirty work, including private intelligence operatives and criminals from both the UK and third countries.
“While altering MI5’s detection challenge, Russia’s use of proxies further reduces the professionalism of their operations, and – absent diplomatic immunity – increases our disruptive options.”
Britain should “expect to see continued acts of aggression here at home” from Russia.
