What does the E or F in front of my number mean?

Nobody has established it. The collector source prints three competing explanations for the Leicester prefixes and picks none of them, so the honest answer is a British razor with prefix E, F, G or H, made roughly 1909 to 1916, with no year derivable from the number.

The maker's archive

Gillette England razors.

The earliest British Gillette factory was in Leicester, and it opened early in 1909. The source believes it probably ceased operating sometime between 1914 and 1915, and that Gillette had vacated the facility by 1916. What it left behind is a set of serial-number prefixes — E, F, G and H — whose meaning no source has established.

Country: UK
Active since
Coverage: No serial tables — component codes only
Dating tier: Codes only
In the archive: 0 series · 2 code systems · 0 models
Years documented: undated

Eras

1909–1916

The Leicester plant

A short life on paper, and a very thin record: the dating table is built from dozens of documented examples, each with the place the number is stamped and the country it was found in, rather than from any factory register.

1930s–1950s

After Leicester

British razors of the letter-code era mostly carry no date code at all, and German ones likewise — the British and German razors had no serial numbers, or no date code after 1951. A British Gillette of the 1950s is therefore dated by the model, the case and the patent stamp.

What dates this maker

Serial prefix — E, F, G or H followed by five or six digits, with the meaning of the prefix not established in any source.
The three hypotheses the source prints for the prefixes — a market, a production line, a country — are all marked by their own authors as hypotheses, and none is chosen.
Patent inscriptions — BR.PAT.No.28763.02 is a British patent of 1902 and PAT.NOV.15.04 is a United States patent of 15 November 1904. Both are lower bounds, not years of manufacture.
Model, case and packaging for everything after Leicester.

Watch out

Do not run a British number through the American table: E is the start of the Leicester prefixes, while in the United States E is 1917. That is a direct false match.
The patent stamp is not a build date: it says the razor cannot be older than the patent, and the same stamp appears inside one and the same prefix range.
A prefix is a factory mark here, not a year letter, so no year can be derived from the number at all.

Gillette England — the serial-number prefixes of the Leicester plant (E / F / G / H)«Gillette's earliest British factory was in Leicester, England, and began its operations early in 1909. As best as we can currently tell it seems that it probably ceased its operations sometime between 1914 and 1915, and Gillette had apparently vacated the facility by 1916.» · 6 rows · Low confidence

Gillette England — the type of patent stamp (a boundary, NOT a year)the source sets the correspondence “Patent Stamp Type 1 = Brit.Pat.No.28763 of 02” · 2 rows · Medium confidence