Whilst I would not dispute the fact that the Bedford Coffee House existed, and that both John Thorpe and the General could have frequented it, I feel obliged to point out that here are several other "Bedfords" in Covent Garden, especailly around ht epiazza there. That's becasue teh whole thing was built on the ruins of Bedford House in a specualtive venture that garnered adn absolute fortune for the Duke of Bedford. As wel as a coffe house, there was a Bedford Street, and also a Bedford House Hotel, just where Lloyd's buildings are now.
I think it possible that both the General and the Thorpes could have stayed in the hotel there.