After looking over and over at the sign, I finally figured it out:
LEVERETT & FRYE - Boundary Warehouse, Bottling Stores and Packing Warehouse.
In one photo archive that I came across while searching for the name in London it turns out that at Powis Mews (place where I found the Ghost Sign) it used to have "a store bottle merchant".
Could it be???? Also while searching for the name itself, it shows as a grocer shop at Commercial Rd. The Square. Bournemouth. Dorset. 1872 - 1913. (See photo)
Leverett and Frye occupied these premises from 1872 until 1913. The terrace was formed by joining two existing buildings, that housed shops that had been trading since around 1850, including Ferrey and Son drapers and Mathew Cox grocers. Leverett and Frye closed in 1913 and a new building, home to Bobby's department store, opened in 1915, with the former Lawrence the Chemist building having been incorporated into the left hand end of the new premises. The dairy to the right remained standing and was finally demolished when Bobby's was extended in 1927.
Bobby's became Debenhams in 1972.
Leverett and Frye had a chain of twelve shops, mainly in the London area, including another branch in Christchurch Rd Boscombe, directly opposite Boscombe Crescent, in the premises now occupied by Argos.
Searching a little more I found at The Brisbane Courier the following: "In February 1893 I read in a small book about the remarkable success which had followed the use of Mother Seigel's Syrup in cases of rheumatism and got a bottle from Leverett & Frye."
I simply LOVE this mystery!!!