If you dont mind driving 30 to 45 mins then plenty in Kent and you are the right side of town, depending on where you stay either up the A2/M" or M20. Have a look at Woolman Wood.
abbey wood is the nearest it is part of the caravan club though so you will have to join i think - check first because it is used by lots of tourists - especially european
dead easy to catch the train in station about half amile away no more or buses
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