I found out the solution.
To forward a podcast client (eg, iTunes) to the new link permanently you must add:
<itunes:new-feed-url>http://yourwebaddress.com/podcast.xml</itunes:new-feed-url>
to the xml file, inside the <channel>
tag. Obviously replacing yourwebaddress.com with the new link to the podcast feed as appropriate.
To tell a podcast client that the podcast doesn't exist anymore you must add:
<itunes:block>yes</itunes:block>
to the xml file, inside the <channel>
tag.
Finally I sent emails to any website hosting links to the podcast and had them removed, and I can now see that there are no new attempts at retrieving the podcast.
Some website's also say 301 errors will inform the podcast client of a new link, so I used a .htaccess rewrite as a fail-safe:
<IfModule mod_rewrite.c> RewriteEngine On RewriteBase / RewriteRule ^path/to/feed http://yourwebaddress.com/podcast.xml [L,R=301] </IfModule>
More info: