At least 58 of the day's arrivals - equivalent to 9 per cent - were cancelled due to the knock-on effect of the problem, which emerged yesterday.
A further 30 departing flights were also grounded from what is the UK's busiest airport.
All the flights affected today were operated by British Airways, which is the largest airline at the west London hub.
The problems at Heathrow compounded the misery for UK air passengers after Storm Dennis caused hundreds of cancellations over the weekend at the start of the half-time getaway.
EasyJet's schedules were heavily reduced, with flights grounded at airports such as Gatwick, Luton and Bristol.
The situation at the airport on Sunday was described on Twitter by one passenger as "utter chaos".
Jenny Nielsen tweeted pictures of whiteboards displaying handwritten flight numbers and destinations.
A Heathrow spokesman said: "Following yesterday's technical issue, Heathrow's systems are stable and the airport is operating as normal.
"We apologise for the inconvenience this caused our passengers.
"Our teams continue to closely monitor our systems and will be on hand across our terminals to provide assistance to passengers."
A British Airways spokeswoman said: "The technical issue with Heathrow Airport's systems has now been resolved but. after 10 hours of disruption across all terminals, we do expect to see a knock-on effect to today's short-haul schedule.
"We've introduced a flexible booking policy and have brought in extra colleagues to help our customers get on their way as smoothly as possible."