Changes at the BBC end broke the BBC iPlayer Radio program for a couple of weeks. The BBC were kind enough to help when I got round to asking, and it should all now be working again.
However, you now get thirty days of radio programmes, not just seven days, so my program takes a while to process all the programmes and display them. Be patient and it should get there.
Thanks to everyone who alerted me to the problem, and the BBC staff for helping out!