There is a large free car park behind the dunes, north Seaton Sluice. People park and unload horses there. The beach looks good, but there are areas of almost quicksand where it is wet. We used to walk the dog there and you suddenly sink into a hole. One person nearly lost his small dog to one. Luckily he saw it fall in. You need to talk to other horse riders about where to avoid. There is also a sandbank which is exposed at low tide. You walk on it, and the tide comes in rushing in behind you. Don't get cut off.
Extra to above, went by late morning today on the bus. Two trailers on the parking area, too far apart to be together. Looked like they were packing up. One a hairy coloured the other had a cart alongside. Weekend mornings are the time to catch people, but check tide tables. If you are on facebook there is a group for bridle paths and in that area.