UPDATE: To close off the thread.
Ordered a new water pump and thermostat plus housing. Total cost £75. Removed old pump and stat by removing the pulley wheel which connects to the rotary part of the pump which then connects to the pump itself. This is where the power steering pump should be on most of these engines but it just seems to be a separated part of the pump, due to the power steering being electric on the Z4. The old pump was seized and the rotary part would barely turn. So yep, definitely the pump! Stat didn't look too great either.
The job was very straightforward in the end, in total 9 screws. All accessible from above the engine bay. The most difficult part was removing the pulley due to it being seized on. The new pump and stat went in very easily.
Refilled with coolant and system bled. A steady needle on the temp dial and hot air our the air vents.
Thanks for your help with this Enuff-zed.