Now that is strange: whilst using Google to look up the origins of this admittedly somewhat bizarre British saying, the first record returned was:

Untitled
everything.blockstackers.com/everything.pl?lastnode=Amsterdam&node=pissed%20as%20a%20fart

... which looks like a quite familiar domain name.

However I digress. This is a fairly common phrase in the UK meaning fairly intoxicated, or more precisely, very very drunk indeed. In fact british slang seems to have a huge number of terms for this state of being, including (but not limited to) bladdered, drunk as a skunk, sober as a judge (this is what we call irony!), pissed as a newt, Brahms and Liszt (rhyming slang), wankered and no doubt many more which I can't currently remember.

Oh, and Google was of no help at all in finding the origins of the phrase. Sorry.