Sky Leisure Aviation are down there.
I know them as I used to fly from Redhill (at Redhill Aviation) and Sky Leisure is owned by the same people. Give them a ring and ask to speak to Tuhin (the CFI).
Shoreham is busy on the radio, but unlike Goodwood or Redhill, it DOES have a tarmac runway, which helps when it's wet (i.e. a lot of the time at the moment).
Your only other option down that way is Lydd...but that's a bit of a hike from Shoreham.