Update...
My brother-in law is an electronic engineer and whilst not a central heating expert, came round for a few hours and with the wiring diagram and some kit, went through is all, testing along the way.
What he discovered was that the wiring was fundamentally correct and the cyl and room thermostats are working, but the timer was not giving the correct signals (Tempus 6).
Upon further investigation, we discovered a likely bad connection where the timer pins insert into the back plate (he manually jumped two of the connections with the timer off the wall and everything jumped into life). Lots of emery cloth and fiddling later and we got it to work* but it remains intermittent depending on whether we press the unit against the back plat firmly or not, confirming this is (one of) the issues, despite lots of connector and pin cleaning. Perhaps the timer is on the way out (2004)?
In addition to this, we discovered that the 3 port valve was not behaving itself again - despite heat being called for, the valve lever stayed in the left hand position for hot water only, even with the room stat way up high. I also discovered when I first went to it that the lever was loose and in the heating position, despite this not being the commanded status.
*When I say working, it still doesn't command the central heating properly (at all) - when I select heating, nothing happens - but at least when I ask for hot water, it all now works.
Also, from memory, I have never since I;ve lived here (20 years) been able to just request heating only on the timer and it do anything - nothing happens. In order for me to get central heating, I must also switch the hot water on at the same time which doesn't seem right does it? Surely I should be able to just ask for heating but with the water side off and the boiler, pump, 3 port etc do their thing and heat the house?
So - should I bite the bullet and get a new timer AND back plate? If so, what is the cheapest, reliable one? I was thinking of this...
https://www.unventedcomponentseurop...9wb_DvY5xhGJDND39P0Fy4aqetfQZPRhoCIuIQAvD_BwE It seems to do everything I need?
Also looks like the 3 port valve head is intermittently not quite right - are the £30 copy heads from Amazon okay?
Any thoughts on the call for heating only and nothing happening, ever situation?
Thanks everyone for the help so far.