The Lord Sandwich story is probably mythical, though. John Montagu, 4th Earl of Sandwich certainly existed, but the only evidence was supplied a man named Grosley who came up with the attribution, claiming in 1770 to have witnessed Montagu ordering a dish of beef between two slices of bread in London during a 24 hour card game session.
Unfortunately for the tale, Grosely didn't arrive in London until 1765, but the word was in use earlier than his arrival or his publication of the tale. Also if such an event even happened, Grosely was unlikely to have been there.
The bread sandwich is far more likely to have been named after the town in Kent, England and was used as a descriptor for many things originating there, strretching back to the 15th century. Food served on bread goes back even further.