Our friends at Etymology On Line has brief entry stating "...The adjective meaning "ill-tempered" is 1639, probably from 16th century. sense of "contrary, athwart," especially with reference to winds and sailing ships.." not much help, I'm afraid....
The 1639 earliest recorded use of 'cross' in this way, as outlined by C above, is from Admirable Events, as translated from the French by Thomas Brugis. The reference actually reads, "The stepmother regards me with cross looks."
In the absence of any evidence that it had been used by anone earlier, perhaps this is where it 'originated'.
And to you, C. It certainly can't be much worse than last summer, which many people in England spent 'submerged'! As usual, our bless�d little corner was spared.