He warned that an attack was highly likely, causing the raising of the national terror threat level from substantial to severe more than a month ago.
"In London we're very, very vigilant and very, very concerned. Every day - as you saw recently, we had to raise the threat level - every day the security services are involved in thousands of operations," he told the Telegraph.
"There are probably in the low thousands of people that we are monitoring in London," he added.
Five men are being held by Scotland Yard on suspicion of plotting a potentially significant attack in Britain.
Johnson said that many of the 500 Britons thought to be fighting alongside the brutal Islamic State militant group in Syria were believed to be from London.
"Probably of the five or six hundred that are out there we think a third, maybe more - maybe half - come from the London area. If and when they come back, we have a real job to deal with them," he said.
"I think he (Churchill) would be appalled by the spectacle of these cowards executing journalists, and I think he would have wanted to do something to set them back a long way and, if need be, to neutralise them altogether. He was a great believer in airpower - don't forget he invented the RAF," Johnson said.
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