Just discovered that ...
... can record from internet radio with the TuneIn Radio Pro app on my iPhone.
(No idea why I didn't spot it before! (I have been using the app for quite a while now.)
A short test (Radio 3 'HD' at 320K) of 5 minutes duration yields an 11 MB file.
Later I will do a 45 minute (CD length) recording to see how much room it takes up. I don't envisage keeping recordings permanently (nor can I import the recordings to iTunes) but this is going to be bl jolly useful.
It also allows timered recordings
I guess you all knew this already (sorry, slower learning curve than many regarding these toys). I love this app!