Hi si-dog all your cold feeds off the main 15mm pipe to you amenities are on town supply which could be anywhere from 300KPA - 1000KPA depending on the available pressure and the area you live in. The main 15mm pipe into the header tank after this is alright but not good. You do not mention any valves, if there was a limiting valve on the main 15mm supply pipe before entry to the house, say 350KPA- 500KPA will give good cold pressure, but the main coming out from the header tank and into the HWC could be 20KPA-30KPA depending on the height of the tank from the HWC. what you have now is unequal pressure. To get equal pressure you may need to lift the tank up to about 30- 50 meters, which could be difficult. The cold pressure is forcing the hot water out your vent pipe, if it is open vented, thru the tap fixtures, or you may have main pressure tapware, giving poor performance.
One option is to isolate the header tank all together, and have the main 15mm pipe supply go straight into the HWC, via a valve train, e.g isolation valve, non-return, filter, pressure reducing valve, isolation valve then into HWC, this will give you equal pressure and excellent pressure if the tapware is appropriate. Depending on the pressure reducing valve rating,  3.6-7.2KPA , a 350KPA-500KPA limiting valve on the main 15mm supply going into the house before the first branch off will remendy your problem.
The black pipe with copper fittings sounds like Quest pipe, which is about that time used in the 40,s. The grey pipe could be Dux or Polybute,which is commonly used today. Both pipes comply with industry standards.
The second option is to replace the low pressure cylinder with a mains pressure cylinder and also isolate the header tank.
I hope this helps.
 Grenville