The francophiles have probably already spotted the "Alex Singer" auction 120218873738 on french eBay. I got detailed pics from the seller who claimed to have bought it used in 2005. To make it short: It is painted like a Singer with original decals end even nicely done lug lining but it is not a real Singer. It might be one of the mysterious el-cheopo bikes sold by the Singer shop in the early 70s but I don't believe even that. Nothing fits, lugs, fork crown, drop outs, the rack looks horribly home brewn. I guess it's just a repinated Gitane or something like that.
Dirk
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Dirk Feeken
Heidelberg
Germany