a pipe stat is neccesary to ensure that the cylinder does not overheat and switches on the pump to the rads to disapate the heater through the rads
Completely wrong. The cylinder is prevented from overheating by the radiator(s) which are part of the gravity circuit and therefore permanently on, this is usually the one in the bathroom. This radiator has to be sized appropriately depending on the boiler heat output.
Assuming you have a gravity hot water and pumped radiators, and a pipe stat and a room stat only (no programmer or any other controls), then the wiring is: Permanent live to one terminal of the room stat, the other terminal (switched live) connects to the pipe stat. The output from the pipe stat connects to the pump live.
How this works:
If room stat is turned down/off, heating does not work.
If room stat is turned up, then the heating works, provided the gravity return from the cylinder is above the set temperature (usually around 45C).
If the return from the cylinder falls below 45C, the pipe stat turns off, which turns the pump off.
This means the heating only works when there is a suitable amount of hot water, otherwise the heating system would take all of the heat from the boiler, leaving the hot water cylinder cold or barely warm.
None of this has anything to do with frost stats, which as already said, can't be used with wood stoves. The part number you posted earlier is a frost stat, so if you have that, it is of no use to you.
Installing these thermostats and the wiring is notifiable work (part P).