At least seven more flights were grounded, including four to or from Edinburgh, with passengers tweeting angrily about missed connections to other flights and the lack of staff on hand to assist.
BA also cancelled three flights today between Glasgow and Heathrow, and one Aberdeen-Heathrow service.
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The airline said the problem was a “hardware” issue and not caused by a cyber attack.
Passengers had criticised the "absolute chaos" at Heathrow on Saturday, with people stuck on planes after landing at the airport and baggage piling up.
But the anger continued today, with passenger Keith Bohannon tweeting just after 7am: “At Edinburgh airport expecting to fly to Nairobi via LHR with @British_Airways but flight is delayed by over 5 hrs so we will miss our connection.
"No one here to help passengers to rebook and no answer on the phone lines.
"I thought I was flying with a world class airline?”
Another passenger, Duncan Wilson, replied: “Stuck in the same nightmare situation having checked in at Edinburgh airport.
“@British_Airways seem to have a total disregard for their customers!"
A BA spokesperson said: “Our teams have worked around the clock to resolve the technical issues we've experienced, and the vast majority of our flights today are due to operate as planned.
"Unfortunately, with some of our crew and aircraft out of position as a result of the weekend's disruption, we've regrettably had to cancel a small number of short-haul flights.
"We've been in touch with affected customers to apologise and offer them the choice of a refund or to re-book onto another service.
"We're asking customers due to travel with us today to check ba.com for the latest flight information before they leave for the airport and to check in online if possible.
“We are deeply sorry for the inconvenience our customers have experienced and thank them for their patience and understanding during this incredibly frustrating period.
"We're doing everything we can to get them to their destinations as soon as possible.”