This route is superb - it traverses one of the best stream passages in the the Ease Gill System, visits some very obscure bits of passage, and manages to avoid the Poetic Justice Pitch, which is normally milling with university students. Also, once you're given a clue about the location of the connecting passages, it is isn't too difficult to find your way through.
From Stop Pot make your way downstream. This is best done by following the water, but in higher water conditions, a low bypass crawl may be found a couple of metres above the water on the left hand side of the choke (not recommended!). Once in the stream way, make your way to Eureka Junction, and turn left. This passage soon divides into two, the left hand branch leading into Wretched Rabbit Passage, and the right branch leading into Pierce's Passage. Turn right, and after a few metres you'll drop down into the Pierce's Passage streamway. Make your way up this until you reach a large run-in of boulders on the left. Follow the stream beneath it to reach a junction where most of the stream enters from the left. Straight on leads to Poetic Justice, but we keep with the stream and enter Lower Trident Passage. This soon develops into a superb stream passage, paralleled for much of the way by well decorated high-level oxbows.
It's well worth going to the end of this streamway to view the atmospheric White Line Chamber, an impressive aven in dark limestone with a prominent calcite vein piercing the wall, and twin waterfalls thundering in from above. Your next challenge is to get top the top of the right-hand waterfall.
To achieve this, back-track for about 30 metres to a corner where there is a passage leading off from a shelf about 3 metres above the floor on the (true) left hand side. There is sometimes a fixed rope hanging down here. Climb into the passage, and follow it until it reaches an oblique T-junction, with the floor of the new passage a metre or so beneath you. Turn right. After another few metres, you'll arrive at an aven six or seven metres high. This currently (November 2012) has a rope hanging down. If you have prussiking gear you can climb the rope. Alternatively, a ledge a couple of metres below the lip can be easily reached by climbing up a few metres back and traversing round. A short heave then reaches the top to emerge on the lip of the right-hand White Line Chamber waterfall. We are now in Upper Trident Series - an interesting and complex area which is well worth a full day's exploration in its own right.
Follow the main passage upstream through a low section into a well-watered chamber. Turn right. From the chamber there is a passage descending off to the right - ignore this and follow the main passage through a rift. You will then pass another passage descending off to the right. Almost immediately after, there is a short climb into a crater - descend this, and follow a boulder crawl for a few metres to a ledge overlooking the modest Battle of Britain Chamber. You are now in County Pot. Standing on this ledge, looking out over the chamber, the way on is a descent through some boulders on the left down at floor level. This leads rapidly into a larger passage, which joins the main County streamway a few metres upstream of Spout Hall.
The most direct route back to the surface is to turn left towards the Showerbath, but more fun is to turn right down Spout Passage and follow the stream down to Platypus Junction. Here Spout Passage combines with Razor Passage to become North West Passage, down which the stream flows. Turn left into Razor Passage, and follow the stream back to Broadway. Route finding through some breakdown chambers is a little challenging, but you can't go too far wrong. At one point, the impressive Butterfield Passage brings in most of the water from the right, with the entrance being marked by a prominent limestone pillar (The Toadstool). Ignore it and keep to the left passage.
Once you get back into Broadway, you will find the climb back up to the County Pot entrance series on the wall opposite.