They were designed by a famous architect, Mr. Barry, I seem to recall--not for anything in particular--just expensive villas closest to the Crystal Palace!
Falkor - they were designed by the distinguished architect John Norton who also 're-modelled' Tyntesfield near Bristol (an amazing Gothic Revival mansion acquired a few years ago by the National Trust). What they were for is an interesting question - they were built on the edge of Crystal Palace Park in order to finance the park (sounds familiar?) and Norton lived in Sydenham whilst they were under construction. They are now part of one of Bromley's conservation areas, although in the 60s there were moves to demolish them!