One of the things I really wanted to know, when I listened to Oscar Williams' Album of Modern Poetry (1959), was whether or not Reed's "Naming of Parts" was different than the other recordings I had already heard on other albums.
For instance, the Smithsonian Institution's Global Sound offers 99¢ downloads of audio samples and music from almost every country in the entire world; offering everything from tribal music to fiddle tunes, including spoken word records. It's an amazing cultural archive.
One album in particular, Folkways' Anthology of 20th Century English Poetry (1961), has poetry by Reed and his contemporaries John Betjeman, Roy Fuller, Laurie Lee, C. Day Lewis, W.R. Rodgers, and Vernon Watkins. The liner notes for Part II (.pdf) state that these recordings were 'directed by V.C. Clinton-Baddeley, and made by Edgar A. Vetter at 22b, Ebury Street, London, S.W.1, Summer 1958' (Google Maps).
I've listened to "Naming of Parts" on both the Anthology of 20th Century English Poetry and An Album of Modern Poetry, and I can safely report that they are definitely two different recordings. Not just different: the Smithsonian's copy of "Naming of Parts" is vastly superior in terms of tone, quality, and clarity. It does sound a bit like he's reading in an empty Tube station, but (in my opinion) Reed gives a more powerful performance on the Folkways' record. The track is only 99¢, and you can get the whole album for just $9.99.
But you don't have to take my word for it. You can join Smithsonian Global Sound and listen for yourself, or just explore what they have to offer. A quick search for "poetry" brings up 59 albums, and 801 tracks!