I'm sorry I haven't heard of it. There is a Kitcher's Copse at Frost Lane (just opposite what was once ButtsBridge Farm which (my 1st cousin x5 removed) John Clasby sold in 1848) This was counted as either Fawley or Dibden at various dates
Did you know that most of the town of Hythe once belonged to Fawley Parish? Dibden Church (to the North) and Fawley (to the South) are the only really old churches in the area and you may find that "Fawley" is a deceptive location and may not really mean the village centre at all