According to Wikipedia Kent is particularly rich in smock mills. It also says they got their name from their resemblance to a person wearing a smock. Actually I worked that one out for myself, but it was nice to have it confirmed.
The Woodchurch mill dates- in its present form- from 1820- though there are records of a windmill in the village as early as 1660 and on the present site in 1729. It used to have a twin- and old photos show them side by side. This is the white mill and the twin was the black mill. The black mill was used as an observation post during WWII and was demolished in 1946. The white mill seems to have been largely rebuilt- though along traditional lines- in the 1980s- and is in working order.