Has "wasp" always been pronounced the way it is?

The dialect of my home town has “wasp” pronounced with a short “a” sound, similar to the “a” you’d get in cat. Mentioning this to my girlfriend, she also said that in the dialect of the Cotswolds near Gloucester, where she is from, this is also true.

Has “wasp” always been pronounced the way it currently is in Standard English, or are these two dialectical differences holdovers from an earlier, more common, pronunciation?

The Online Etymology Dictionary says it came from the old English wæps or wæsp. The latter would have been pronounced the way you mention in your first paragraph.

So you rhyme “wasp” with “asp”? I’ve never heard that. Where are you from?

The North of England. Actually, thinking about it, a lot of words beginning “wa” are pronounced the same way (water, for instance — listen to about 40 seconds into this recording). The OED link BigT gave also seems to suggest “water” was pronounced with the short “a” sound at one point.