There are several solutions to this, which revolve around a VPN service or getting a proxy server in the country you're trying to reach (either connecting via a friend's machine located in that country or using a commercial service you can rent for a monthly fee).
The Tor network provides just that, but for free. It was set up as a means of providing anonymity and
"defend against a form of network surveillance that threatens personal freedom and privacy, confidential business activities and relationships, and state security known as traffic analysis",
however, besides the usual traffic we can also use it to route our streaming movies through it, same as somebody in Syria may use it to upload content to Youtube. If you're not familiar with the Tor project I urge you to read the documentation on the website and several other places that explain how and why. First you'll have to install Tor, a proxy server (usually Privoxy) and for nice graphical management Vidalia, a management console that requires QT. Most distributions have this available in one of their repositories, or just download the Tor Browser Bundle which is a self-contained Firefox all set up and use it on a Flash drive. A good guide to installation is here on http://www.ubuntugeek.com/howto-install-torprivoxy-and-tor-gui-programs-vidaliatork-and-torbuttonin-ubuntu.html, but there are many around.
Now we come to the meat, because by default to guarantee anonymity traffic bounces randomly around the Tor nodes (proxies), so there's no telling where you will SEEM to be located next. But we want to watch streaming videos in the UK or the US, so we got some configuring to do. The rest of this document is mainly thanks to this blog post by Cherie Hurwitz, credit where credit is due, and you may want to read that one too including the comments section.
1.) To watch BBC ensure that the last server your request is routed through is a server in the UK. Go to https://torstatus.all.de/. Scroll to the bottom of the page, and click “Show Custom/Advanced Query Options”. Under “Require Flags” choose “Yes” for “Exit” and under “Advanced Search” choose “Country Code” “equals” “GB”. Adjust this for any other country if for any reason you only want to exit through nodes in that country. Click “Apply Options”. Take note of all or some of the Router Names of the resulting servers except those marked Unnamed. These are your exit nodes in the UK. It's best to write down several and use the ones offering higher bandwidth first. Be sure to have at least three or four as this is a network run by volunteers and servers come and go. If that one is down use https://torstatus.blutmagie.de/ or http://tns.hermetix.org. These seem to be the only ones where status reports are currently working.
2.) Open and edit your torrc Tor configuration file. Scroll all the way to the bottom and enter the following lines:
If a line starting with “ExitNodes” already exists, then overwrite the line with your new exit nodes.
3.) Make sure you have the latest version of Adobe Flash installed...doh.
4.) Run Vidalia which should connect you to the Tor network. Your proxy server has to be running for this to work.
5.) Launch your browser of choice and configure it to use your local proxy server that you just installed earlier on, normally '127.0.0.1' using port '8118'. Under Firefox you would enter this under Network-->Advanced--> Settings. Enter this also for SSL Proxy and SOCKS Host, and make sure you have an entry for No Proxy for: '127.0.0.1'.
6.) If you cannot connect and get an error that your proxy server is refusing connections most likely your proxy server isn't running.
7.) Tor comes with a button that allows you to toggle the server on and off. However I prefer the quickProxy extension. The original author used FoxyProxy in her example and designed some elaborate rules designed for the local proxy to kick in automatically only when specific web sites were visited. I prefer the simple method and just switch it on with a click when needed. Beware, there's another extension around called QuickProxy, not quite as simple and friendly in my view.
8.) You can go to one of the sites we used to get our exit nodes and confirm that you're anonymized using Tor and it's all working. You should see something like this:
9.) Obviously you're gonna use a lot of bandwidth from people that is going through several nodes, three to be exact, so it's going to be somewhat slower and loading may take longer. However after the initial wait it is usually working fine and streaming movies or news are smooth. Consider giving something back to the community and running your own relay if you can. And remember, Tor isn't just for frivolous stuff like watching movies undetected. A lot of people in countries where vocal dissent will get you tortured, whistleblowers and others concerned about their privacy depend on this for their instant messaging, browsing etc. Spammers are using this too though.
Unfortunately this method doesn't work with Hulu any more. They seem to maintain a list of known Tor exit nodes in the US and if you're coming from one of these IP addresses are blocked.
The BBC only does its IP check in the beginning, so you can disable the proxy again and do some surfing on the side, a bit speedier. However, when watching long movies (~2 hrs.) they occasionally implement another check. Enjoy -