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By Simon Browning
Business reporter
British Airways has said continuous high winds over the last few days have made it difficult to unload baggage from its planes.
The airline said stormy weather made opening the luggage hold of aircraft hard, and passengers had faced delays getting their bags after landing.
It has also struggled to land and restock its planes on time, affecting inbound and outbound plane movements.
BA apologised for "letting people down".
It added that items of machinery needed to offload bags could not be be operated in high winds.
Machinery such as scissor lifts, that are needed to load catering trucks on to aircraft, also cannot be used because of the danger they pose.
The high winds of Storm Eunice on Friday and Storm Franklin on Monday have delayed many flights because of the difficulties landing aircraft.
BA said every time a flight could not land, it had to circle above the airport and then try again. But every time this happened it caused further delays to flights due to leave in the following hours.
It also said some staff had not been able to get to work because of the storms.
"We are extremely sorry to all our customers who have been disrupted during the extreme weather conditions in the last few days," the airline said.
"We know we have let people down, and that isn't good enough, but can reassure our customers that we are doing absolutely everything we can to improve the situation."
It said it was operating the vast majority of flights as planned but, due to bad weather in the UK and Europe, it was still experiencing some disruption and had been forced to cancel or delay a number of flights.
The airline added that it was "working round the clock" to reunite passengers with their luggage.
Customers due to travel on short-haul services on Monday can rebook flights for free, it said, while those whose flights have been cancelled can get a full refund.
Heathrow is not the only airport being affected by high winds. On Monday, Manchester Airport said it had diverted nine flights because of stormy weather.
It is understood the planes were waiting to land before being diverted.
The airport says it has had no impact on departures.