It looks like by default get_iplayer will only download tv shows by default, the start script (/home/nobody/start.sh) needs inside the docker image needs to be updated to include --type tv,radio
You can do the following to get it to work:
Create a file on your server with the following line:
type radio,tv
edit the binhex-get-iplayer container with an additional path.
Container path: /home/nobody/.get_iplayer/options
Host path: /mnt/user/appdata/binhex-get-iplayer/options
The only problem is the files remain inside the incomplete dir and are not moved because start.sh script moves files ending with mp4.