Heathrow airport operator BAA has said the problem with the software used for checking-in baggage at Terminal 4 has been resolved.
Problems emerged on Tuesday leading to delays for thousands of passengers who had to travel with just hand luggage.
British Airways (BA) said economy and premium economy customers should not bring luggage to be checked in.
BAA said the system was returning to normal but it advised passengers to check with their airlines.
The computer problem had serious consequences for the BA's World Traveller (economy), World Traveller Plus (premium economy) 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.
Terminal 4 handles baggage for BA's long-haul customers.
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