The airline cancelled all short-haul flights from the airport until midday on Saturday and said there would likely be delays to long-haul flights.
It said there was likely to be “further disruption during the day” at Heathrow, Gatwick and London City airports.
BA advised customers to check the website for the latest flight information before heading to airports.
The airline said the problems were caused by hardware issues and not a cyber attack.
BA’s website and app were inaccessible for hours on Friday evening, preventing customers from checking in online or booking flights.
Paul Charles, chief executive of travel consultancy The PC Agency, said the continuing technical issues "don’t fill consumers with much confidence.”
“BA needs to be transparent on what’s causing these issues and how soon they will be fixed,” he said.
The airline has experienced problems before with its check-in systems.
Earlier this month, Heathrow Airport revealed it had endured its worst financial year in history in 2021, with passenger numbers falling to a near 50-year low due to the UK’s Covid-19 travel restrictions.
Heathrow said the current number of passengers was 23 per cent behind forecast.
Despite the sluggish start to the year, the airport – Europe’s busiest before the pandemic struck – expects to meet its target of 45.5 million passengers by the end of 2022.