Newsreaders speak more slowly and also tend to accentuate their speech, especially when they are speaking to a diverse audience.
I am a native speaker and if I were to pronounce Britain on its own, I would pronounce the "t" quite clearly. If I were to pronounce it in a sentence, the "t" would be a lot more subtle. If I was speaking to an international audience, I'd imagine I'd make more of an effort to pronounce the "t", but this might well be down to the fact that I would be speaking more slowly.
Pronouncing the "Br" in Britain requires the speaker to push a lot of air from their mouth. In order to give the "t" an equal amount of focus in the word "Britain", the speaker would be forced to pause slightly before its pronunciation. Since we typically like to speak quickly, we don't bother with the short pause and pronounce the "t" with less focus instead.
It is common in languages for certain letters in certain words to loose their accentuation over time. This is because people can still understand what word they are referring to even if this letter looses focus. This is why silent letters appear in the spelling of certain words. For example in Old English, the "k" was pronounced in "know", as was the "g" in "gnaw".