Slips for the Mudway.
Medway bridge marina. Good slip but strong current at all but HW +/- 1hr. Pontoon berth and parking. Not sure of charges.
Gillingham Pier. If he catches you I think it's about £5 each way. A gentle slope so not good for car launching. Access HW +/- 3hr with soft glutinous mud at the bottom.
Gillingham Strand. A poxy place to launch. Ok at hw but avoid if possible.
I use the public slip at Sheppey Yacht Club
. Access is about HW +/-4hr. Free of charge. Be careful when the wind has any north in it, the breakers appear from nowhere! Parking on Marine Parade.
A bit further east along the coast towards Halfway and Minster is Bartons Point which again is exposed to a northerly and they charge you to park. Access is about HW +/-3hr.
Queenborough. Access at all states of tide but awkward at HW +/-1hr. The slip starts off ok but levels off for a couple of hundred yards before curving to the right and then its ok again. There are two areas off to the side where you can pass/prepare. Launching and car park is free. There is a pub at the top of the slip with another just down the road. To the west is the all tide pontoon. £1 per person to enter the pontoon (tokens from either pub or Queenborough Yacht club). No overnight mooring.
Best marina is Chatham. 24hr lock access, £15 a night for my 5.4m.
Alternatively there is a public slip at Whitstable, free of charge but parking can be very busy. Access HW +/- 3hr and about an hour from the Medway. Herne Bay is further east. Good wide slip with car & trailer parking. Slip is free but parking is not. Access HW +/-4hr.
Hope that helps!