As with any proxy/VPN, using something like that means trusting that party with any and all traffic you route through them. They could potentially capture, track, or perform MITM attacks on any activity you perform using their service.

At any rate, I'm fairly sure the this would be a violation of BBC's terms, particularly if you're not actually a UK resident and paying the TV license/tax. And their programming is available legitimately here on BBCA and other stations (some public television stations even have authorized free streaming, though it's a season behind).

ElanaAhova you might take a look at Acorn Online,   http://acornonline.com/default.aspx

Once you get there register, it's free to do so.  After that click on Acorn TV.  You can stream BBC shows and movies there, they allow you to stream one episode of the shows listed or movie free.  You can join and become a Premium Member, $2.99 a month or $29.99 a year and watch as much as you want.  There is also a free trial for 30 days.  I like BBC TV, we have Dish Network Satellite TV and get BBC America and three different PBS channels which show some older shows and I now Acorn TV. 

It's worth a look if you like BBC TV and you don't need to worry about things like is it legal.