This is actually really interesting. When I was young and stupid I decided to walk from Brighton to Hastings (about 13 hours). And what struck me at the time was that you simply couldn't walk the coast, which I thought was a bit weird. Now I'm old and stupid I'd like to do this whole route. I bet there are people planning to walk/run it.
World's longest coastal path opens in England to the public
Alas it sounds like this is not also a cycle path
Yes! An excuse to break out one of my favourite jokes....
Two bits of black tarmac go into a pub. They order drinks at the bar and look around for a space to sit. The pub's full but there's a table free in the corner next to another table that a bit of red tarmac is sitting at.
"There's a table free over there" says one bit of black tarmac to the other.
"I'm not sitting over there!... that guy's a cyclepath!"
This may now also be one of my favourite jokes
Ben
Charles ☭ 
is a Green