Just called the hotel, and they don't have their own car park. However, they can recommend parking spots in the area for about 35 pounds a day.
Driving to London would give me the flexibility of not depending on train schedules. I had planned on leaving the car at the hotel for the time I am going to be there.
Since I will be having lunch in Benenden, what would make most sense? Ashford, Gatwick or another option that I am unaware of. I want to make sure I leave the car in a relatively safe environment.