It looks like the BBC radio player uses the Flash plugin, have you tried (re)installing that?

Do you see the Lego block icon at the left end of the location/address bar indicating that a plugin is used?

You can try these steps in case of issues with web pages:

You can reload web page(s) and bypass the cache to refresh possibly outdated or corrupted files.

• Hold down the Shift key and left-click the Reload button
• Press "Ctrl + F5" or press "Ctrl + Shift + R" (Windows,Linux)
• Press "Command + Shift + R" (Mac)

Clear the Cache and remove the Cookies from websites that cause problems via the "3-bar" Firefox menu button (Options/Preferences).

"Clear the Cache":

• Firefox/Tools > Options > Advanced > Network > Cached Web Content: "Clear Now"

"Remove the Cookies" from websites that cause problems.

• Firefox/Tools > Options > Privacy > "Use custom settings for history" > Cookies: "Show Cookies"

Start Firefox in Safe Mode to check if one of the extensions ("3-bar" menu button or Tools > Add-ons > Extensions) or if hardware acceleration is causing the problem.

• Switch to the DEFAULT theme: "3-bar" menu button or Tools > Add-ons > Appearance
• Do NOT click the "Refresh Firefox" button on the Safe Mode start window

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

Thank you both for your help - clearing the cache seems to have sorted out the issue. I am most grateful