"where the omnibuses now stop outside the Elephant and Castle"
were originally horse-drawn public carriages, the first of which was established by George Shillibeer in 1829. They were initially also known as 'Shillibeer's' and later on as 'buses'. The era of the horse-drawn omnibus finally came to a close in 1911, after which the service was motorised.
The Elephant and Castle (known colloquially as 'The Elephant') is the name given to a road intersection in the London borough of Southwark. It is also the name given to the surrounding area.