Scotland Yard said last night that images of two of the packages had been circulated to mail sorting offices and transport workers.
Police responded to suspicious packages at Waterloo train station and office buildings at Heathrow and London City airports on Tuesday.
Security sources emphasised investigators were keeping an open mind and said he devices did not appear to be very sophisticated.
Following reports the packages had been sent with Irish stamps, a statement from Irish police said: “An Garda Siochana are assisting the Metropolitan Police with their inquiries.”
Scotland Yard said it was working “to ensure the safety of the public and staff working at transport hubs and mail sorting offices”. The organisation said: “We have shared images of the exterior packaging of two of the devices to aid staff in identifying a potentially suspicious package.”
All the packages were A4-sized white postal bags containing yellow Jiffy bags and appeared capable of igniting a small fire when opened, the Metropolitan Police said.
Widely reported images appeared to show the partially burned package destined for The Compass Centre at Heathrow and another sent to Waterloo.
The stamps appeared to be ones issued by the Irish postal service for Valentine’s Day 2018 featuring a heart motif and the words “Love Eire N”.
Both senders’ addresses were given as Dublin, with the one addressed to Waterloo appearing to add Bus Eireann.
The bus and coach operator said police had not been in touch. A spokeswoman said: “Bus Eireann are currently not aware of this and we have no further comment.”
The source of the images was not clear.
Scotland Yard said officers were treating the incidents as linked and are keeping an open mind regarding motives.
No-one has been injured in the three incidents and no arrests were made.
Officers first received a report of a suspicious package at The Compass Centre, a building near Heathrow Airport’s boundary, shortly before 10am.
“The package was opened by staff at the building, causing the device to initiate,” Scotland Yard said.
“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.
A Heathrow spokesman said flights and passengers were not affected by the incident.
British Transport Police were later 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 secured the device.
One slightly shaken-up man who was among staff outside the Network Rail office said he found that package.
Asked about the discovery, he said: “I’m sorry, I’ve been told I can’t talk about it.”
The station was not evacuated and trains continued to run as normal, but cordons were in place outside on Cab Road.
Shortly after midday, officers were also called to a report of a suspicious package at Aviation House at London City Airport.
The package was not opened, the building was evacuated and specialist officers made the device safe. The building reopened.
A spokesman for London City Airport said Aviation House was a staff-only building about three minutes from the terminal and no flights or passengers were affected.
Mayor of London Sadiq Khan said: “Our thanks go to police, security, transport staff and all involved for their swift actions to keep our city safe.”