I've found a few tasty morsels on Google Book Search in two publications put out by the Booksellers Association of Great Britain and Ireland, The Publisher and The Bookseller ("The Organ of the Book Trade"). Both the Publisher, and later The Bookseller, listed entries for the week's literary programs on the BBC, so here we find, in this volume from 1947, listings for February 23 at 10:38 pm, "Time for Verse: Compiled by Henry Reed, the poet", and for June 17 at 6:55 pm, "Book Review: Henry Reed on Shelley and Cecil Day Lewis".
In the Bookseller for April 20, 1963, however, we discover something of a mystery: a reference to Reed and several other authors being asked to contribute something to something:
It says: 'The contributors, who, among many others, include Nevill Coghill, Richard Hogart, Henry Reed, Alan Ross, Stephen Spender, and Philip Toynbee, were asked "to..."' (p. 1642). But the limitations of snippet view do not allow us figure out exactly what these authors were contributing to, or even what they might have in common.
Nevill Coghill was a literary scholar known for his modern version of the Canterbury Tales, which was first produced for the BBC; Richard Hoggart was an academician, who was a witness at the Lady Chatterley censorship trial; Reed, Ross, and Spender were, of course, primarily known as poets; and Philip Toynbee was an experimental novelist.
What were these writers contributing to, and what was they asked to do? Trying to find a library in the States with a 1960s run of the Bookseller is an exercise in exasperation. University of Georgia libraries? At least I have the exact date and page number, which means I can try to get a photocopy through interlibrary loan.