Traces of some letters can seen in the upper part of this sign but not enough to make much sense. The only word still fully visible is at the bottom:
A picture of the house taken c. 1955 was published in the book Petersfield. Then and Now (it is also available on the Francis Firth website). By the time it was taken the butcher's had been converted into an antique shop. The tile with the bull's head, which is still there, is clearly visible under the shop's window but with the sun straight on the façade, the painted sign is very hard to spot. Back then the entrance to the shop was on the left of the window, while the present door was only a window.
Location: The Street, South Harting, West Sussex / Picture taken on: 02/08/2009