Online since October 2014, the BBC Genome project contains the text of program listings in the Radio Times from 1923 through 2009.
The search function at the top of the page allows keyword (and advanced) searching, as well as browsing by service, year, and issues in pull-down menus.
The search result for "Henry Reed" yields 1,013 results (many belonging to a popular band leader of the same name), but setting limits in the advanced options for "Radio only" brings us to Reed's possible first billing, for "New Poems" on August 3, 1944: 'The ninth of a monthly selection of very recent or unpublished poems : "The Jungle," by Alun Lewis , and "Philoctetes," by Henry Reed.'
The listings are OCR text which contain many errors, and there are no images from the original magazines — but the project does allow users to submit corrections (or notice of changes to the original schedule).
Read about the BBC's Genome at the About the BBC blog.