Disruption was reported at airports including Heathrow, Gatwick and London City.
The airline said it was having to use a manual check-in process which takes longer than the computerised system.
One passenger described the bag drop area at Heathrow Terminal 5 as “almost at a standstill”.
The disruption comes around two months after more than 670 flights were cancelled due to a power failure over the spring bank holiday weekend.
BA issued a statement shortly before 9am stating that the problem had been resolved and passengers were being checked in as normal.
It went on: “We are sorry for the temporary check-in problems which caused some delays for our customers first thing this morning.
“This issue is now resolved and our staff are working flat out to help customers get away on their holidays.”