This is an example of one of those things you change, forget, and then it comes back to bite you later.
After reading about yet another Adobe Flash security hole, I decided to follow the herd and change the options in the Chrome browser to make the running of plug-ins "Click to Play". This is set in the Settings->Advanced->Content Settings->Plug-ins radio button dialog.
About a week later I tried to listen to BBC live radio via Chrome. It appeared to start to play, although there was no sound, and then a little while later, gave an error message:
I figured an intermittent problem and ignored it. However, the same thing happened the following week, so I realised it was my problem, not the BBC's.
I found that "Listen Again" was working fine, but needed me to click
to allow Flash to start... Ah! Luckily, Chrome allows the creation
of exceptions to the general rules, so I added
[*.]bbc.co.uk
as an allowed exception for plug-ins and
music returned.