Heathrow is among several European airports hit by a cyber-attack affecting an electronic check-in and baggage system.
The airport warned of possible delays due to a "technical issue" affecting software provided by Collins Aerospace to several airlines.
Brussels Airport said a cyber-attack on Friday night meant passengers were being checked in and boarded manually, while Berlin's Brandenburg Airport also reported longer waiting times due to the problem.
RTX, which owns Collins Aerospace, said it was "aware of a cyber-related disruption" to its system in "select airports" and that it was working to resolve the issue as quickly as possible.
The company added: "The impact is limited to electronic customer check-in and baggage drop and can be mitigated with manual check-in operations."
It said the attack hit its Muse software - which allows different airlines to use the same check-in desks and boarding gates at an airport, rather than requiring their own.
Lucy Spencer said she had been queuing to check in for a Malaysia Airlines flight for more than two hours, and that staff were manually tagging luggage and checking passengers in over the phone.
"They told us to use the boarding passes on our phone, but when we got to the gates they weren't working - they've now sent us back to the check-in gate," she told the BBC from Heathrow's Terminal 4, adding that she could see hundreds of people queuing up.
Another passenger, Monazza Aslam, said she had been sat on the tarmac for over an hour "with no idea when we will fly", and had already missed her onward connection at Doha.
"I've been at Heathrow with my elderly parents since 05:00," she said, adding: "We are hungry and tired."
Heathrow said additional staff were at hand in check-in areas to help minimise disruption.
It added: "We advise passengers to check their flight status with their airline before travelling to the airport and arrive no earlier than three hours before a long haul flight or two hours for a domestic flight."
Transport Secretary Heidi Alexander said she was aware of the incident and was "getting regular updates and monitoring the situation".
Brussels said there would be a "large impact on the flight schedule", including cancellations and delays. Long queues and large crowds could be seen at the airport on Saturday morning.
Europe's combined aviation safety organisation, Eurocontrol, said airline operators had been asked to cancel half their flight schedules to and from the airport between 04:00 GMT on Saturday and 02:00 on Sunday due to the disruption.
It said "similar issues" were affecting Heathrow and Berlin, and that "measures may be required".
There have been nearly 100 delays in and out of Heathrow as of 10:00 BST on Saturday, according to tracker FlightAware, while there have been nearly 70 delays in Brussels and 15 in Berlin.
Travel journalist Simon Calder said that "any disruption is potentially serious" at Heathrow, given it is Europe's busiest airport, and that "departure control is a really complex business".
He told the BBC: "These things are all interconnected, so a little bit of a problem in Brussels, in Berlin... people start missing connections, planes and passengers and pilots are not where they are meant to be, and things can get quite a lot worse before they get better."
