If you look Carfax up in the dictionary, you will be told it comes from the latin quadrifurcus, four forked, a meeting of four ways, but in Horsham's case it is more probably derived from Scarfoulkes, the previous name for this part of town. There are only two towns in England with a Carfax. Horsham's is effectively the town centre.
The following two images were taken just before Christmas 1998. Hence the grey weather. Each looks towards the bandstand from different directions.
The Carfax is well endowed with estate agents, banks and building societies, and a variety of small shops, including a rather excellent Cheese Shop, a Butcher and, of course, a Post Office.