You need a VPN, the sort that can give you a UK IP address. If you just want to watch TV, and are not concerned with a VPN anonymous security features, you could try a browser add-in. There are several free ones available for Firefox and Chrome. I don't know which one work with the BBC, so I suggest you try several (one at a time, as they can sometimes interfere with each other if you install more than one), until you find one that works.
There is an add-on called "Hola.org" that might work for you, but there have been some "issues raised" concerning how the company operates, so I suggest doing some reading online before deciding whether or not to use it.