Entry into Heathrow's terminals was also heavily restricted and passengers were being checked at the entrances by security guards and armed police. Anyone who left was prevented from re-entering, passengers said.
Travellers met with chaos once inside the terminal buildings, as both international departure and arrival halls heaved with people.
As passport control allowed a trickle of passengers through to the gates, BA closed check-in desks and began ordering all passengers on short-haul flights set to depart before 3pm to leave the airport.
Later, the airline cancelled all short-haul flights to and from the airport.
Michael and Margaret Burns, both in their 50s and hoping to transfer from New York to Aberdeen with their three children, said they were unsure what to do.
"Apparently, if you leave the airport, you won't be allowed back in. We're just sitting here wondering what to do: get a train, hire a car or just sit it out," said Margaret.
"All we've heard is there was a security alert because of a bomb plot," said Michael. "We're not upset [about the chaos]. Staff are doing their best and trying to make us feel safe. Of course there's chaos. We've been told we won't receive our luggage for a few days. But we understand. Everyone is in the same position."
Stood next to one of the empty check-in desks, a BA customer services agent, Rizvana, explained that most passengers were being asked to leave the airport.
"Long-haul passengers can stay, but everyone else must go," she said. "We're giving everyone a card with a customer services number they can use to re-book their flights. But they have to leave the airport and will not be allowed back in."
Transfer passengers with BA whose flights had been cancelled were being sent to nearby hotels, a source from the airline said.
However, five Spaniards in their 40s who had hoped to catch a transfer from Bangkok to Barcelona said they had been told they would need to wait until Saturday for their next flight to Spain.
"At the start there was no one giving out information, but things have improved," said one woman in the group. "But still, we're in a queue and we don't know why - or where it will take us. One [member of staff] told us the situation was out of their control, and we would have to work out our own itinerary or wait until Saturday. We're just lost. We want to find a solution but if we leave the airport we won't be let back in, and this is where our luggage is."
Imran Choudhry, 29, accompanied his wife to the airport at dawn for a flight she had booked to Boston.
"I guess that, as we were checking in, something must have kicked off," he said.
"We were told no one could take hand luggage and there seemed to be an air of panic. From all that was going on it was clear there was something serious happening," he added.
"Reluctantly, we checked in my wife's hand luggage, but for the last few hours we've just been told to wait."
At Manchester airport, emergency security measures delayed departing flights for up to three hours early today and 10 flights to Heathrow were cancelled.
More than 200 holidaymakers were taken off a Thomas Cook flight to Lanzarote after a passenger found a threatening message on a magazine in a seat pocket. It read: "This plane is going to crash today."
Passengers returned to the departure lounge while the plane was searched.
By late morning, delays were reduced to a maximum of 90 minutes, with passengers enduring long queues to check in and then to pass through security, where they were required to remove shoes, jackets and belts.
All 15 flights to the US went ahead.
More than 37,000 passengers were expected to travel in and out of the airport on 340 flights.
All three Manchester terminals were patrolled by sniffer dogs and armed police and, as at Heathrow, passengers were issued with plastic bags in which to carry only the essential items allowed on aircraft.
"We have not faced a situation like this since 9/11," said an airport spokesman. "But it has been amazing - I have not heard or seen anyone complain. They just seem to get on with it. People have been very understanding in the circumstances and we have not needed to do a lot of explaining."
Staff used the public address system to apologise for the delays, adding: "Your security is our first priority."
