Apple T.V. / BBC Global iPlayer

It sounds as though some of you do not know about GLOBAL iPlayer. This is not the same as ordinary iPlayer which is illegal to watch in Spain, although many people do obtain it by using a proxy server. Global iPlayer is a legal app that you pay for and can be used on an iPad or iPhone. It shows some current BBC content but mainly has good quality past programmes and series. We have a slow broadband speed, usually below 2 meg, and it works almost faultlessly on my iPad 1. We know that we can use an adapter to connect an iPad 1 to a TV and view the Global iPlayer app on it, but we have read that you can also get this app on an Apple TV ( a small box that you connect to your T.V.) and then you can stream the content directly to your T.V. using AirPlay. What we want to know is has anybody tried this and does it work?

Thank you all for the useful information. So, it sounds possible, but I would still like to know if there is anyone out there who has actually tried it, particularly with a low broadband speed.