The swans are probably not panting. In fact, the sound you are hearing is the flapping of their wings. We are not sure if you are hearing Mute Swans, Bewicks or Whoopers. In the U.S., the Tundra Swans were at one time known as the Whistling Swans because their wings made a whistling sound as they flew. The Bewick Swans are the European subspecies of the Tundra Swans. So, they are probably not the swans you are hearing.

This would leave the more common U.K. swan (Mute). Therefore, the whomp, whomp, whomp of their wings flapping is probably what you are hearing. The Regal Swan