A newpaper article says, "There are other reasons to doubt the global warming alarums."

What's the difference between an alarum and an alarm?

The letter u?

Actually, I don't think there's any difference; it's just a variant spelling. Poets may find alarum fits their metre better than alarm, or the writer may feel that it has a better resonance.

Is this chiefly British? At least one dictionary (MW) said it was British, though others didn't. I haven't seen it spelled that way.

I wouldn't know if it is chiefly British, but I'd say that it's likely. It has an archaic ring to it (sorry) so that might give the impression. "Alarums and excursions" is the stage direction used by Shakespeare to indicate battle scenes.

It's also in the OEDILF; and 'alarum' has a limerick of its own here!