Another option is to start at Horsham train station near to Gatwick and then hike the High Weald Trail all the way to Rye. It also has a train station, goes to Ashford one way, towards Brighton, etc the other way. Undulating walk, lovely views, attractive villages, great pubs, walk across fields, woods, through orchards of apples, plums, pears, cherries, etc. A very varied walk, the whole length would take up to 10 days, possibly more.