Here is another way that does not involve hosted files, and uses GreaseMonkey and FoxyProxy to emulate what I did to make it all work.
1. Download the addons for for FoxyProxy and GreaseMonkey.
https://addons.mozilla.org/en-US/firefox/addon/2464
https://addons.mozilla.org/en-US/firefox/addon/748
2. Next we need to configure FoxyProxy to be used in Patterns mode so that when the request to get a particular URL from the BBC is made it is made via the UK Proxy. This URL contains the token to view the video.
3. From within FireFox select the Tools Menu then FoxProxy menu and then the Options Menu.
4. Click the Add New Proxy button
5. In the Proxy Name Field enter BBC iPlayer Proxy
6. Select the Proxy Details Tab
7. Select the Manual Proxy Configuration Radio Button
8. In Hostname and Port enter the Hostname and Port (and select if it is a SOCKS Proxy and version if using SOCKS)
9. Select the Patterns tab
10. Click the Add New Pattern button
11. In the Pattern Name field enter "BBC iPlayer Media Selector Pattern"
12. In the URL Pattern enter
http://www.bbc.co.uk/mediaselector/*
13. Leave the WhiteList and WildCards radio buttons selected
14. Click the Ok Button
15. Click the OK Button
16. Go to
http://www.darkedges.com/bbc/iPlayer.user.js
17. When prompted click the Install button to add the GreaseMonkey Script
18. Go to
http://www.bbc.co.uk/iplayer/ and select a video to stream
19. A preview image will show and and a white "Click to play" button should appear and now your should be able to view the video. First the ident appears and then the video, which is not streamed via the proxy.
For step 8, the best place to look is here
http://www.xroxy.com/proxy-country-GB.htm