Gulls, especially black headed are very unlikely to be predators of cygnets - even from hatching cygnets are pretty big and adult swans are very protective. Foxes are a possibility on land but are almost always easily seen off by the much bigger and heavier adult swans. This isn't the case for otters, which can additionally come up from underwater and nab a cygnet (or duckling) by the legs and dive down again, so they are a fairly likely candidate.
Otters & foxes between them are a likely part of the reason why the black headed gull colony at Cors Caron, which numbered over a 1,000 pairs in the 1970s, has never re-established. Only a few pairs attempt nesting most years, sometimes none at all. Something hoovers up all eggs & hatched young quite early in the season every year.