According to Graham Gibberd's On Lambeth Marsh , land bounded by the current Hercules Road, Kenington Road and Cosser Street was leased by Sergeant Major Philip Astley in the 1780s. He developed his own house Hercules Hall, Hercules Terrace, where William Blake lived, and the Hercules Tavern, which still exists. Hercules Terrace or Row became the current Hercules Road.
Until redecoration in 1996/97 the pub was a kind of branch office of the Central Office of Information, serving fine spirits, hot and cold dishes and excema. The Central Office of Information is decorated with a crude mosaic of Hercules, doubtless in complete ignorance of Astley or why anything is called Hercules.
Sergeant Major Astley was a circus strongman, who performed "Twelve Trials of Hercules" in his own theatre, Astley's, on the site of the current St. Thomas' Hospital nurses home on Westminister Bridge Road. His son took it over, and it remained in operation for many years, part of the Lambeth tradition of cheap theatrical spectacle that continues to this day with shameful excesses such as the Royal National Theatre. See also footnote 220 on the Old Vic.
Dickens describes the vulgarity of the crowd and the inferiority of the spectacle at Astley's in Sketches by Boz.
Astley's went through a number of name changes, often like the National called "Royal", and remained open until 1893. It was finally closed, like so many buildings south of the river, for being a disorderly house.
Read the tea leaves, National.