Eels may
seem a good candidate for the factual basis of monster reports. They are long and flexible "like a plesiosaur's neck" and they are also capable of wriggling across damp ground or through long damp grass. Keep adding a bit to the length on each iteration of the story to allow for wishful thinking, and they can become huge!
Also, there are various true or nearly true stories about congers, morays, and electric eels that present "eels in general" as quite formidable.
However, eels undulate from side to side, rather than up and down, and are bottom feeders which makes them unlikely to stick their heads and necks out of the water. Most eels spend most of the day concealed in crevices and hunt at night.
Until there is a clear photo of a fresh water eel substantially longer than a metre, I'm going with that being more or less their maximum length. It's a small jump to imagine one 10% bigger, but I'd need more to go on before I accepted that there "may be" undiscovered eels 3 times as big.
I posted this story elsewhere in the forum, related to Windermere. I do not wish to add further comment to it, but I think it is a fun read.