Boris Johnson has said thousands of potential terrorists are being monitored by the security services in London.

The London mayor said 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.”

His comments came as police chiefs warned officers to be more vigilant in the face of a heightened terror threat for police. Five men are being held by Scotland Yard on suspicion of plotting a potentially significant attack on Britain.

Johnson said that many of the 500 Britons thought to be fighting alongside Islamic State (Isis) in Syria were believed to be from the capital.

“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.

The mayor, who has written a biography of Sir Winston Churchill, claimed that the wartime prime minister would be authorising air strikes on Isis if in power: “I think he 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.”

Meanwhile, Iain Lobban, director of GCHQ, suggested that it now took three times longer to trace terrorists online in the wake of disclosures made by former National Security Agency contractor Edward Snowden.

Lobban also told the Telegraph that sharing intelligence with a greater number of nations was necessary: “It’s nonsense not to share with the French. This is not Blitz Britain. We sure as hell can’t lick terrorism on our own.”