I vaguely recall that the original reactor experiment with just the right spacing of uranium metal lumps and graphite moderator may have been natural uranium

I think this is correct but finding a source which says that seems to be tough. However, Wikipedia does explicitly confirm that the successor to CP1 did initially use unenriched uranium.

Edit: This article (pdf) seems to confirm it. They couldn't even use pure uranium but had to use uranium oxide. No mention of any sort of enrichment is made.