Green’s Dictionary of Slang

Greenwich barber n.

[such retailers ‘shaved’ the sand for their product]

a seller of sand from the Greenwich sandpits.

[UK]Grose Classical Dict. of the Vulgar Tongue n.p.: Greenwich barbers, retailers of sand from the pits at and about Greenwich, in Kent: perhaps they are styled barbers, from their constant shaving the sandbanks.
[UK]Lex. Balatronicum.