Right, once you get everything ready you tell the neighbours what you're doing and not to use the loo as you do the job, or you'll end up with jobs on your toilet floor.
You need to free the spigot of the bend into the wall. The stone/brickwork around it should be large enough to allow you to make quite a big hole through the wall. Keep all the big bits that come out of the wall so you can use them again to fill the hole back in when you're done.
Once you get the spigot cleared you'll find it easy enough to waggle around the pipe that's atached to it. The waggling around will ease the lead joint but it has to be done firmly but gently so that the pipe begins to move freely but doesn't break the sides of the old spigot, so move it little bits at a time with your hands and don't bash it about with hammers and things.
When the pipe is moving quite freely you should find it easy to get a narrow chisel in the joint to dig the lead out. It takes a bit of patience and a lot of jabbing with the chisel for the first ten minutes or so until you see any great progress, but stick with it for this time and you'll be able to remove the pipe in one go and keep it in one piece.
Every time you chip a load of lead out, waggle the pipe around in a circle again until the pipe gets looser and looser. The lead wil get easier and easier to remove the more you do this. When you get down to rope caulking is the time when the pipe will lift in one whole piece. Remember to waggle the pipe firmly but gently and don't move it huge distance or you'll break the sides off the spigot.
When you get the caulking rope is the time you go tell the neighbours not to use their loo while remove the old pipe and install the new one. Once you have the new pipe in place you ca nuse the old caulking rope to wrap around the pipe and press it down into the spigot to keep the new plastic pipe in the centre of the spigot end. Whe nthe pipe is firmed in with rope you can fill the spigot with a sand and cement mixture and support it until it dries out and goes solid. Or you can fill the joint with silicone sealant from the gun type tubes you can buy. This too needs to be supported until it cures off and this can, in both cases, take up to 24 hours.
Keep the end of the pipe that stick into the room covered with a damp cloth or jam it with screwed up newspaper to keep the smells out of you house and allow your neighbours to use the loo again without stinking your home out with last night curry.
Because you're on the ground floor of this building, you should be able to do this job in a couple of hours from start to the point where you're letting the pipe joint set hard and everyone above using their loo again.
Tools needed:
Hammer and brick bolster (to remove the stone, mortar fro maround the spigot in the wall) Narrow wood chisel 1/4'' (under 10mm wide that you'll never use again on wood, so get a really cheap one just for this job) Tube of silicone sealant or gutter seal and an applicator gun Any other tools needed to remove things from around the inside where the pipe is
Please don't try to use the lead again because when it's hot it melts its way through the plastic pipe quite easily. :-))
Good luck with it.