In March, a licence was granted for the first time in England to release two pairs of beavers into the wild at Little Sea.
Previous licences had only been granted for enclosures.
Beavers need areas of deep, fresh water but have been known to travel along the coast to look for new lodgings.
The National Trust believes the female swan about 5km (3 miles) around Old Harry Rocks on the Purbeck coast after leaving its lodge.
“We had considered that that was a route that was possible but we thought it was a bit too far,” Mr Crisford explained.
“Seeing one turn up in a stream in Swanage town was a big surprise.”