It's the same all along that coast too - Rye is miles from the sea, but operated as a major port through to the end of the 19thC.
The Isle of Oxney was an island in its own right though, and a 10 minute visit to the area shows how small it would have been, one look at a map confirms it!
I have an old book written by a guy who toured Kent on foot, and the placenames would suggest that way back there was more inland water than there is now - mills and small jetties way upstream from any navigable water nowadays suggests that the water level was at least higher, for whatever reason.
The Darenth is a good example - 18 years ago it was drying up, literally down to a trickle at best and in some places totally dry http://www7.caret.cam.ac.uk/gw_57.jpg caused by a lot of extraction and diversion of water upstream. That section in the pic is 500 yards downstream from a Roman grain store and mill, and at least 8 miles from the most upstream villa, of which there were probably 10 alternating along the bank. Every one of them placed by a usable river.
Now it's healthy again, thanks to a lot of pressure on Thames Water [water pressure!].