There could be a number of things going on all at the same time here. Here is just a coulple of possible senario's.
The washer in the ballc0ck in the header-tank could be worn or the arm needs adjusting as it may be filling the header tank up too much & even to all-most overflow point. This will then alter the designed head of water calculated for the rising thermal of the expansion / vent pipe and it becomes comprimised and circulates round the feed and expansion pipes, too and from the hot water cylinder, thus constasntly replenishing the hot water cylinder with cold water.
or...
you may have a leaking tap washer under you're bath or a leak anywhere on the hot water pipe work you are not aware off, and again the hot water is constantly been replaced with cold.
There are other possible things but these are 90% of the times the main problems we encounter.
As you say the first poster did not recognise the system you have and their answer was for sealed systems only. You will find you have no relief valves installed.