Look what turned up in the New York Public Library's Berg Collection of W.H. Auden material: Henry Reed's personal copy of Auden's Poems (1933). That's the second edition of Auden's first published poems from 1930, submitted to T.S. Eliot while he was at Faber and Faber.
The library catalog record states the copy 'contains ownership signature, "Henry Reed, 1943" on free endpaper'. That would mean this was a book Reed had with him during the war years, while he was stationed at Bletchley Park (previously). No word on whether there's any marginalia, however.
The book was a gift given to the NYPL in June, 2007, from Eric H. Robinson. Could that be the Eric Robinson, historian and literary scholar, long claimant to the copyright (Guardian) of the poems of John Clare (1793-1864)?