All services at UK airports should be back to normal by Friday, after 19 flights from Heathrow were cancelled on Thursday by British Airways.
In total, the airline has now cancelled more than 1,300 flights - 1,000 at Heathrow - since new security measures came in a week ago.
Its backlog of displaced customer bags is down to "several hundred" and would be cleared by the end of Thursday.
Airport operator BAA is facing calls from BA for compensation.
But BAA said it "acutely regretted" the disruption.
It is still advising passengers that strict security measures remain in place at all UK airports.
While restrictions have been eased, it is not a return to the security situation which existed before police said they had thwarted an alleged bomb plot, BAA said.
And it called on passengers to be patient, to allow extra time and to arrive prepared.
Displaced bags
Earlier, some reports suggested as many as 20,000 passenger bags may have been displaced at Heathrow in the past week.
MAX HAND LUGGAGE SIZE
The extent to which passenger luggage had been misplaced first emerged on Tuesday as measures allowing people to take one item of hand luggage on flights, subject to size and content restrictions, kicked in.
BA is considering seeking compensation from BAA for the number of cancelled flights, accusing it of not having had an adequate plan to deal with the security alert.
Similar criticism has been voiced by other airlines, including Virgin Atlantic, but it has stopped short of calling for compensation from BAA.
Virgin, which says its flight schedule is now back to normal, said questions needed to be asked about whether more could have been done to speed up searches at airports.
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