Add a BBC Podcast to iTunes
It sounds like Winamp has claimed podcast/RSS feeds, rss://, on your computer. This means when an podcast/RSS feed is clicked, Winamp is launched rather than iTunes.

The BBC's Podcast help suggests copying and pasting the podcast link directly into iTunes:


  Subscribing using iOS, Android or Window
  
  Select your operating system. Once you have installed your chosen
  software simply click on the relevant button and the software will do
  the rest.
  
  Subscribe using a feed reader
  
  Clicking on RSS will take you to the actual podcast feed page.
  
  Some browsers may display instructions at the top of the page in which
  case simply follow them.
  
  Or, you can copy and paste the feed URL into a new feed in your
  podcast software or feed reader - just look for buttons or links
  marked "Add feed" or "Subscribe".