I just played with Google Translate and Britain translates as بريطانيا while British translates as البريطانية. I don't speak Arabic either so I'm only guessing here, but the script for 'British' looks something like Il-Britaini, which I believe would mean 'Of Britain'
I could be wayyy off.
For the Airways part, it translated into الخطوط الجوية - two separate words. Translated back into English gave me 'Airlines' - the الجوية part of the script is 'air' and الخطوط is 'lines'
If the Arabic announcement uses English words in it though, why not just say British Airways in English?