My grandmother (born 1914) always told me her mother was half Romany. Her mother could have been told she was Romany descent for all I know, but Gran wasn't prone to stories and it was one she mentioned a few times, just not details because I guess she didn't know.
Surnames I have:
Lavender - I know this is a travellers surname, but not one I can link to the area. Another researcher was quite determined in their opinion that the Lavenders of this area had never ever been gypsy folk.
Davis
Burgess
Leeves
These are further back in the tree:
Piper
Aukett
Brook
Bray (New Malden)
Gurr
Sanders
Duffell
de Verrye (right back in 1553, married a Lavender)
Main locations: Warbleton, Alfriston, Brighton, Worthing, Goring, Broadwater, Burwash, Brighton and surrounding parts. I've got back a 100 years if not more on most branches, found a few religious names dotted around (Esau, Levi, Eli, Job) but none in a lump that's helpful.