The problem is, a swan doesn't have the necessary strength to generate the lift required for takeoff from a hard surface; they can only take off unassisted from water. It's a common occurence for them to see a smooth surface covered in a thin film of water and think it's a river so they land.
It doesn't help having that canal along the south side of Heathrow; it seems to attract hundreds of swans and as they're all the property of the Monarch, you can't just go out and shoot them (even though persons from certain East European countries think you can.)