I have asked the East Riding council for details of where their boundary lies on the coast and in the River Humber. I got a rather formal reply that was informative. Part of their reply says that they lease the land that lies between mean high water mark and mean low water mark from the Crown Estates for much of their North Sea coastal boundary. This led me yesterday, at Peter's suggestion, to ask the Crown Estates for more information.
This morning I got a friendly reply with some suggestions and some information. There were helpful questions which may lead to receiving more information, including, perhaps, a map. The guy who answered had read this blog to try to find what I was interested in and seems to be trying to help rather than being forced to help.
One thing he has offered is that they will show a visitor to their London office the extent of their land in their GIS system. I don't go to London much nowadays, but maybe some other OSMer who is interested might like to.
I'll see what his final response is but I expect it will be good given his helpful start so far.