the first is the UK way of saying the word, the second the US..

Actually both pronunciations are used in the UK, Helen, just by different bunches of people. It's partly a regional thing, and certainly used to be a "class" thing.

I suspect that people over here who say "gar-idj" (yeah, and accepted that the opposite is "gar-aaj" without a d) would also pronounce cinema as ending with "-uh" rather than "-aa". At least I do.

Be interesting to see other Brit responses here.