The only mentions of the building and decorating firm of James Rugg & Son I could find date from 1933 and 1948, in The Electrical Journal and Charles White's The Royal Borough of Kensington respectively.
It is rather unusual for the name of a telephone exchange -Frobisher- to be written in full, the custom being to put the first three letters only. In this case, potential customers would have had to dial the code 370 for FRO. The Frobisher exchange served the Earls Court area (if the name of most exchanges made sense -in some way-, in this particular case it escapes me as I haven't found any connection between this part of Kensington and the English navigator and explorer Martin Frobisher).
Given its good state, this ghost sign was certainly painted after the war, possibly in the 1950s if not later. In any case no later than 1966 since that year the Director System for telephone numbers (three letters followed by four numbers) was replaced by All Figure Numbering.
James Rugg & Son Ltd
Sanitary & Electrical
Location: Kenway Road / Pictures taken in November 2012