Aine,

The term Sloane comes from Sloane Square. Found this on a London Tourism site. Hope the html is not frowned upon here.

Sloane Square SW1 Nearest Tube: Sloane Square This square, on the boundary between the districts of Chelsea and Belgravia, is synonymous with wealth. The name comes from Sir Hans Sloane, an 18th Century physician and naturalist. His collection of unusual objects and artefacts became the core of the British Museum's collection when he died in 1759. In the 80s this square gave birth to the term 'Sloane Ranger' meaning the wealthy bright young things of Britain's upper classes - the most famous of all being Princess Diana. Although the term is no longer used as much, it does give you an idea of the reputation of the area. In the square you will find the Royal Court Theatre, Peter Jones department store and lots of stylish cafes and bistros frequented by their very rich and chic clientele.

I'd disagree with the 'bright' bit but apart from that, it's fairly accurate...

Clare