Why does BBC Radio Player fail in Safari on my Mac? Sorry this is a UK-only issue.

The BBC have a Flash-based player for their live radio on the following page:

http://www.bbc.co.uk/iplayer/console/bbc_radio_fourfm

This works fine in Google Chrome on my Mac, but in Safari, the Flash elements in this page fail to load, and the radio does not play.

What could be causing this? Do other Safari users see it? How does one diagnose a Flash problem in a web-site?

I have no extensions, nor Safari plugins installed.
Clearing Safari's cookies fixed the problem!