The ad appears in a two-page spread of the December 25, 1954 issue of The New Statesman and Nation, part of section called "Christmas Diversions." This elaborate hoax by the editors is entitled "Publishers Anonymous," and it's laid out to appear exactly like publisher's advertisements for new books by frequent contributors, being released specially for the Christmas holiday. It only takes the reader a moment to realize they're being had, but that's all that would have been required to grab their attention and get them to read the entire feature. Follow the linked image to my Flickr set to see the whole thing, with close-ups, and explanatory notes for some of the more obscure inside jokes (I'm lucky if I understand half of them):
There's a running gag where all of Elizabeth Bowen's reviews for The Tatler proclaim the books are "Absolutely delightful!" (Bowen preferred not to give negative reviews, and only reviewed work that she enjoyed), except for a book on critical reviewing, which Bowen finds "Instructive!"
The invented publishing houses include: Bourne & Griffin, Fathom House, Hussif Publications, Ivy and Fitzroy, Parlour Press, and Wildenstein & Pargiter, with this jape about Cyril Connolly, editor of the journal Horizon:
Then there's this delightful send-up of W. Somerset Maugham, who studied medicine before becoming a novelist, from "Frerechild Books":
The caricature was drawn by Victor "Vicky" Weisz, seen here at the British Cartoon Archive. Here's the entirety of the New Statesman's "Publishers Anonymous," scanned into a .pdf.
Even though it turned out to be all in jest, and I practically made a fool of myself, finding these pages is still significant. Reed was thought well enough of to be incorporated into the joke, which is certainly flattering. His inclusion places Reed among his friends and contemporaries, like John Betjeman, Elizabeth Bowen, Edward Sackville-West, and Angus Wilson. Reed's radio plays were apparently considered so popular they were replayed with almost ridiculous frequency. The comparison with Gogarty means that Reed was renowned as a wit of nearly Olympian proportions. And most importantly, the title of Reed's book secures him as a member of a group of writers and artists who frequently met at a pub off Corporation Street, Birmingham, in the 1930s: the Birmingham Group.