The Bow Street Runners were known as Robin Redbreasts.. They had a blue dress coat and a bright red waistcoat. They were known as `redbreasts`. Could this mean that others knew them as Robins? Source - The Cassell Dictionary of Slang.
i thought it was postmen because they used to wear red jackets-- a bit like a shorter version of the chelsea pensioner coat. i thought the bow street runners or early peelers wore blue coats