Are you planning to follow the coast? The SWCP goes about 350miles I think to Poole (can't remember where it actually ends but there is a good official website with loads of info. I haven't walked much of it but the bits I have done on the South Coast are lovely.)
Then you could(somehow) join the South Downs way further inland which goes from Winchester to Eastbourne (also has a good website). It is then fairly easy to walk to Hastings, Rye, Camber and via Dungeness to Dover via Hythe /Folkestone. (There used to be a closed bit just before Hythe but not sure if this is still in use a MOD training).
As said, it is a pretty long way and very variable terrain so although 16 to 20 miles a day is not that much to contemplate, doing it day after day for hundreds of miles is a different challenge.