As one that lives close to the Kent/Sussex border and the area that you speak of, I can confirm the woods there are home to wild boar. I have seen them in the flesh, as well as plenty of tell-tale signs of their presence, including rubbing posts, tracks, wallowing holes, rooted up farmland, etc.
See this website which will give you mopre information on what to look for and where:
Wild Boar in Britain
hth.