Armed patrols have been stepped up to protect potential terrorist targets such as shopping centres. Among them are the Westfield mall in Shepherd's Bush, West London, and Kent's Bluewater complex, the Sun reported.
London's Metropolitan Police's firearms unit has been ordered to keep within a three-minute drive of possible targets, including Canary Wharf, a major business area.
The alert comes after reports of Al Qaeda terrorists planning a copy of the Mumbai attacks in India two years ago, when gunmen killed 166 and injured hundreds.
Civilian staff at the Met's emergency call centres have been briefed on how to deal with a "mass shooting". The strategy has been codenamed Operation Plato.
Metropolitan Police chief Sir Paul Stephenson had also warned that "terrorists search for weaknesses and vulnerabilities".