I don't live on Canvey, but I stumbled on the site while I was browsing concrete barge stuff.
I did use to live in Rainham though and also used to walk down to the barges on occassion.
Don't know if this info will be of any use to anyone, but, about 30 years ago, several of the Rainham barges had private property warnings on them and I can remember a sign that said they were the property of 'The Layer Shipping Company', no less.
One of them, toward the western end of the group, also had a bit of wooden superstructure (AKA a shed) on it, which I think someone used, off and on. I can also remember there being a chap (in his 50s or 60s then) that used to turn up in a Land Rover and go onto the Shack Barge.