Flight BA303 was due to take off for London when the incident occurred, with police and fire engines surrounding the plane on the tarmac, reports the Guardian.
One passenger said those on board were informed by the pilot that an individual had made a direct threat against the aircraft.
Passengers were led off the plane and individually searched by armed officers, with luggage in the hold searched by dogs.
Travellers had waited on the plane for about an hour, at first being told there were "technical issues".
"They were then told the plane was to move to another part of the airport. Then they noticed police and fire engines quickly surround the plane and dozens of armed officers and firefighters got out," Anderson tweeted.
"Every single person and every single item of baggage was searched. That took around an hour," he told the BBC.
British Airways said: "The safety and security of our customers and crew is always our top priority... We would never operate a flight unless it is safe to do so."