Timing cases for the Singles had many changes over the years. Before he died, the late Ralph Hawkins began to assemble an article for Cheval outlining their evolution but he was unable to resolve the complexity of the changes before he died. I have dallied with the idea of building on Ralph's work (which I have) but so far have not acquired the examples of timing cases to be able to write and photograph a definitive article on the subject.
For 1957 you need a case where the top screw housing has a straight line from its tangent point to the main tangent point of the case. The one mentioned on Ebay features this. Earlier cases had the top screw housing as a "circular" addition to the top of the case. For 1954 (I think) and/or 1955/56 some genius deleted the second ball valve on the feed side, the one in the timing cover. Presumably after a spate of seized engines, this was re-instated for 1957 and a second ball valve was finally fitted on the return side as well. See Service Bulletin No 125 for details: http://www.arielownersmcc.co.uk/members ... %20125.pdf
Other timing cases will fit (but most will lack the two locating dowels of the 1957 version) and work well enough, but I can't recommend too strongly having the second ball valve on the feed side. Originally, of course, the second ball valve was provided by the pressure regulator.