OK, to keep Lethal happy, here is a logical explanation for how this region of South London came to have such a peculiar name.

In the middle part of the last millennium the European Royal Families often inter-married -- after all, who was a princess fit to marry if not a prince. The Spanish Princess Royal is traditionally named the Infanta da Castille. Reputedly one of these Spanish Princesses, on her way to London to meet her potential future husband, rested overnight at an inn in this area and the local inhabitants were so impressed with her grace and beauty that they named the inn in her honour. Over time this became corrupted to Elephant and Castle and gradually as London expanded outwards, this name became associated with the entire area.

As to the lack of either elephants or castles here, well that's hardly surprising considering it's now a quite run-down area of inner city London. To most people these days Elephant & Castle is either a tube station or a very large roundabout surrounding an ugly shopping centre.

The Infanta of Castile story is itself the folk etymology in this case. It is believed Elephant and Castle is actually named after an elephant. In India an elephant has a howdah on it, the cabin arrangement in which you sit while riding it. This became known to the Crusaders, but the image was converted by heraldic artists at home into a castle, or to be more exact a tower. In heraldry when an entire elephant is depicted it is almost always an "elephant and castle".

Like any heraldic bearing, it could be used on signs to indicate ownership or overlordship. So pubs get to be called Elephant and Castle because that's the inn sign. There was one such at the place in London, which now gets its name from it.

In this case, the pub was founded in about 1760, on the site of a smithy used by the Cutlers' Company. This also used the sign. Cutlers make knives and knives have ivory handles: this may be why the motif was used.

British royalty has two connexions with Castile, the first being Eleanor of Castile (mar. 1254, d. 1290), queen to Edward I, who however was centuries before the term infanta was used; and an infanta who was once engaged to Charles I. She did not however set foot in England, as far as I know.

In addition to the other writeups in this node, Elephant and Castle is also a restaurant chain with locations scattered across Canada and the United States. The restaurants are styled after UK pubs, and serve much of the same traditional fare, British cuisine (oxymoron?), like fish and chips, shepherd's pie, not to mention bangers and mash, in addition to more American-style bar food. You have to appease the masses, I guess...

Beyond the menu, Elephant and Castle also carries a decent variety of imported beers and scotches.

As an addition or clarification to iain's explanation of the original term, the Elephant and Castle website has a differing explanation, although the concept is basically the same... it perhaps makes more sense, at least aurally.

Around the 14th century in far off merry old England, there lived a noble family from the Province of Castile in France. The family had a daughter whom they were to marry to a rich English prince. Then, as now, the rich and famous were the subject of gossip in all the inns and taverns. The comings and goings of the family from Castile were of great interest and everyone was awaiting the outcome of the situation.

Not too many people are aware, but England was bi-lingual at that time. It was common for the nobles to converse in French. For this reason, the Castile's daughter was know as L'Enfante de Castile - the child of Castile.¹

Addendum: Rose Thorn and I have come to the conclusion that the Castile in question is probably Spanish after all, so that explanation, wholly or in part, may or may not be bullocks.

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¹http://www.elephantcastle.com/restaurants_ec_description.html