People flying from Heathrow's Terminal 4 are facing delays because of problems with baggage handling software.
BA aircraft at terminal 4 (library picture)
British Airways, the main airline based at the terminal, said economy and premium economy customers should not bring luggage to be checked in.
It says such passengers will only be allowed to travel if they bring a maximum of two items of hand luggage.
Airport operator BAA said it was "confident" a full service will be resumed on Thursday.
It said that passengers should still check on its - or BA's - website for the latest information before travelling to Terminal 4.
The problem first emerged on Tuesday and has serious consequences for the airline's World Traveller (economy), World Traveller Plus (premium economy) and transfer passengers.
BA's website says that these passengers, travelling from Terminal 4, should not bring luggage to be checked in.
If they do they will not be allowed to travel. They are, however, allowed to bring two items of hand luggage, and complete their journey.
The airline said that Club World and first class passengers are not affected by the baggage restriction, and it advised customers to check its website for the latest developments.
A BA spokesman said: "We would like to apologise to our customers for the disruption as a result of the failure of the airport's baggage system in Terminal 4."
The terminal handles baggage for the airline's long-haul customers.
BAA told the BBC that its engineers believe they can either fix the software problem affecting two baggage sorting machines, or install a temporary system allowing baggage to be sorted manually.
"BAA is now confident that a full service will be able to be offered to all passengers [on Thursday]," said the airline operator.
BA said passengers due to fly from T4 are eligible for a refund, can re-book to a different destination or travel on a later date.
It has published full details of the options available to customers affected on its website.