Dover did not have a pier when this text was printed so passengers were rowed from ship to shore by local boatmen. This picture of Dover Harbour c1830 shows exposed beach either side of the two harbour walls so presumably the channel between the walls was too shallow (at  least at low tide) for steamers of the sort shown in the top right quarter of this image

https://doverhistorian.files.wordpress.com/2013/11/th-dover-harbour-c-1830.jpg

Steam boats were faster than sailing ships so less time was spent at the mercy of the weather and were also less likely to wallow in light airs.

"Them ere white things on the beach" are probably bathing machines within which people removed their clothes prior to bathing.

"Image to yourself a small, snug, wooden chamber, fixed upon a wheel-carriage, having a door at each end, and on each side a little window above, a bench below - The bather, ascending into this apartment by wooden steps, shuts himself in, and begins to undress, while the attendant yokes a horse to the end next the sea, and draws the carriage forwards, till the surface of the water is on a level with the floor of the dressing-room, then he moves and fixes the horse to the other end - The person within being stripped, opens the door to the sea-ward, where he finds the guide ready, and plunges headlong into the water - After having bathed, he re-ascends into the apartment, by the steps which had been shifted for that purpose, and puts on his clothes at his leisure, while the carriage is drawn back again upon the dry land; so that he has nothing further to do, but to open the door, and come down as he went up."
Tobias Smollett 1771

https://wordwenches.typepad.com/word_wenches/2011/08/bathing-customs.html