Barnacles, limpets or gribbles?

The Leafless walked in from a walk by the beach to tell us about a log which had washed in. She said it was full of shells. I thought it might be barnacles. I finished my tea and walked out to look at the log.

It was a freshly broken branch of a tree, and it had been colonized by bivalves. Clearly these were not barnacles or limpets. Were they gribbles? I didn’t think they were. They could be piddocks; those are bivalves. But the piddock shells I got to see in a few days did not look like these. I wonder what these mysterious creatures are. Look at the movement of the shells on the extreme left in the 7th second of the video below: they look like real bivalves.

I wonder if anyone can help me figure out what they are.