Counter-terror police are investigating three packages containing explosives found at Heathrow Airport, London City Airport and Waterloo station.
The “small improvised explosive devices” were found in A4 postal bags, the Metropolitan Police said.
The force’s Counter Terrorism Command is treating it as a “linked series” and “keeping an open mind” about motives.
Irish police are assisting the Met as the Heathrow and Waterloo packages had Republic of Ireland stamps.
Heathrow’s Compass Centre was evacuated after a package was reported to police at about 09:55 GMT.
The device set fire when staff opened the bag.
Scotland Yard said: “The packages – all A4-sized white postal bags containing yellow Jiffy bags – have been assessed by specialist officers to be small improvised explosive devices.
“These devices, at this early stage of the investigation, appear capable of igniting an initially small fire when opened.”
A Heathrow spokeswoman said the airport would assist police investigation into the “criminal act”.
The Gardaí confirmed it was also assisting the Met.
Ireland’s postal service identified the stamps as its “Love & Wedding” design for greeting cards, wedding invitations and thank-you cards.
The Compass Centre, which is an office for Heathrow staff rather than part of the passenger terminals, remains closed.
About 100 workers were evacuated from City Aviation House at City Airport in Newham after a third package was reported at about 12:10.
City Aviation House is a two-minute walk from the passenger terminal.
Staff returned to the office at about 16:00.
The second and third packages were not opened and have since been “made safe”, police said.
Flights were not affected but Docklands Light Railway trains did not stop at City Airport for about an hour during the investigation.
Ass Ch Con Sean O’Callaghan, from British Transport Police, said commuters should feel “safe and reassured” while travelling.
“Officers will be highly visible on station concourses, on board trains as well as the London Underground network,” he added.
“Passengers are of course the eyes and ears of the network and we want to hear from you if you see something that doesn’t look right.”
Transport Secretary Chris Grayling urged people to report “anything suspicious” to police, while Mayor of London Sadiq Khan added: “Our thanks go to police, security, transport staff and all involved for their swift actions to keep our city safe.”