In his Morgue Peter mentions that Arthur used to have lunch at an ABC, which was a chain of high street cafes. The remodelling of the shop front at 231-232 Fleet Street has revealed the ghostly outline of the old shop sign:"The Aerated Bread Co. Ltd" (ABC). It's just outside the gate way to the Middle Temple, where Arthur had his chambers, and I imagine this is the cafe Peter had in mind.
Another little detail: The BL library catalogue lists the following book: "Law relating to factories and workshops (including laundries, railways and docks) by Mary Edith Abraham, notes by A. L. Davies. 8 volumes, 1896-1905.