Police responded to reports of suspicious packages at Waterloo train station and office buildings at Heathrow and London City airports on Tuesday.
All the packages were A4-sized white postal bags containing yellow Jiffy bags and appeared capable of igniting a small fire when opened, police said.
Scotland Yard said officers are treating the incidents as linked and are keeping an open mind regarding motives.
No one has been injured in the three incidents, police said.
Officers received a report of a suspicious package at The Compass Centre, a building near Heathrow Airport boundary, shortly before 10am.
A statement from Scotland Yard said: "The package was opened by staff at the building, causing the device to initiate.
"This resulted in part of the package burning."
The building was evacuated as a precaution and specialist officers attended the scene to make the device safe.
Police said the building remains closed as enquiries.
A Heathrow spokesman earlier said that flights and passengers were not affected by the incident.
British Transport Police were called to reports of a suspicious package in the post room at Waterloo station at 11.40am.
The package was not opened and specialist officers again made the device safe.
Police were also called to a report of a suspicious package at Aviation House at London City Airport shortly after midday.