Oh good, we are making progress.
Your timeclock has 3 outputs
When Water is on it sends live up the water on wire which connects to the orange of the zone valve (interrupted by the cylinder stat)
When heating is on it sends live up the heating on wire, which connects to the white of the valve (interrupted by the roomstat)
When water is off it sends live to the grey of the zone valve.
When water is on at clock but off at cyl stat, the cyl stat diverts the water on live to the grey.
It seems that your clock is not providing this live for water off although just to make sure that there have been no misunderstanding:
Stick your water to continuous, heating timed, cyl stat to normal position.
Your water will now run untill cylinder is hot and then all will switch off. You will get a bit of heat to the rads because of the valve letting by but ignore this for now.
When heating comes on, it should now operate perfectly normally, room stat will control pump & boiler because the cylinder stat is providing the water off feed rather than the time clock.
If you can get the time clock off put a link wire from terminal L to terminal 1 (htg on) and a link from 1 to 4 (water off)
Dont replace the clock front and power back on. It should all now behave as if you had selected heating only on the clock.
If replacing the clock I would not waste time looking for a exact replacement, people like what they like, loads like honeywell, I prefer ACL
https://www.screwfix.com/p/drayton-lp522-mk4-programmer/20673