The Leaky Cauldron pre-dates Muggle Charing Cross Road. When the road was to be built, the magical community performed Memory Charms on the Muggle builders – protecting the Leaky Cauldron.
The pub was built by Daisy Dodderidge, the first landlady, in the early 1500s “to serve as a gateway between the non-wizarding world and Diagon Alley.” It had a bar, several private parlour rooms, and a large dining room.
To Muggles, the pub appears to be a broken-down old shop front on Charing Cross Road. This, however, was not the case prior to the imposition of the Statue of Secrecy and, in fact, prior to this, Muggle visitors were neither turned away, nor made to feel unwelcome.