Hi farmergiles, it's quite straightforward to get to Priory Rd. from Southern Stream Passage.
About 2/3rds of the way down Southern Steam you come to the waterfall beyond which the passage gets a lot easier (basically just sideways walking). Keep looking up and you'll soon see the start of a passage in the roof. This is Gothic Passage. There is a hand line and traverse on the right at a wedged block, which gets you up into Gothic. Look out for the lovely crystals coating the walls.
Gothic starts off walking height but soon lowers to hands and knees and then down to flat-out just before a T-junction. Turn left here and very soon you reach a flat-out crawl on the right. This is the original dig via which Priory Road was discovered. A short crawl leads to a dip in the floor and then one of those horrible, flat-out, 45 deg., upwards crawls which I find really knackering. This pops you out into Priory Road by Ribbed Vault which is an impressive aven.
Right at the T-junction leads to Resurrection and Maytime.
So basically climb into Gothic Pass., turn left then right.