Flights cancelled from Edinburgh Airport include the 10.15am, 11.30am and 1.55pm, while two flights from Glasgow Airport at 10am and 12.20pm have been cancelled.
From Aberdeen Airport the 7.20am, 9.05am and 10.40am flights all faced cancellation too.
The airline said the problem, which may also cause delays for its customers using Gatwick and London City Airport, is related to a hardware issue and is not because of a cyber attack.
The major outage has caused cancellations and delays of flights, pile-ups of luggage and passengers stuck on planes after landing at Heathrow.
It said long-haul flights are still operating, but customers may experience some delays.
BA’s website and app were inaccessible for hours on Friday evening, preventing customers from checking in online or booking flights.
On Saturday morning, the airline advised customers to check the website for the latest flight information before coming to the airport.
In a statement, BA said: “We are extremely sorry that due to the continuing technical issues we are facing we have regrettably had to cancel all short-haul flights from Heathrow today until midday.
“Customers due to travel later today should check their flight status on ba.com before coming to the airport as we anticipate further disruption during the day.
“Our long-haul services at Heathrow and all flights at Gatwick and London City Airport are due to operate as planned, but customers may experience some delays.
“Our website ba.com is working and customers can check-in online and at the airport.”
Photographs of departure boards in Heathrow Terminal 5 showed few flights boarding, while people complained on social media about a lack of information.
It is BA’s second outage in 10 days.
Paul Charles, chief executive of travel consultancy The PC Agency, said: “Ongoing technical issues don’t fill consumers with much confidence.
“Many people have saved up during lockdown to get away at the first opportunity and some are now finding that computers, not Covid-19, are preventing their getaway.
“BA needs to be transparent on what’s causing these issues and how soon they will be fixed.”