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I originally understood these to be a form of freshwater sponge. But they are in fact peculiar creatures in their own right, being colonies of an enormous number of indivuals.
In summer 2017 we saw a number of these around where South Otter flows into North Otter, and also around where North Otter flows into Rothwell Lake (which is where these photos were taken.) These colonies were about 16 inches in diameter.
The colony below we found in shallow water beside our dock. It measured about 6 inches in length, and had cleary formed around a submerged twig.