Heathrow airport operator BAA says it has solved a problem with software used for checking-in baggage at Terminal 4.
The terminal experienced a major system failure on Tuesday which affected all airlines operating from it.
All passengers flying from or transferring through Terminal 4 can now check their baggage in as normal.
The computer problem caused serious problems for the airline's World Traveller and World Traveller Plus and transfer passengers, who were allowed to travel with a maximum of two items of hand luggage.
The airline said that Club World and first class passengers were not affected by the baggage restriction.
A BA spokesman said: "British Airways would like to apologise to its customers for the disruption.
"The airport operator, BAA, has now restored the baggage systems to allow normal check in processes to resume."
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