Grey wire from 3 port goes to blue wire from cyl stat - no other wires exit from this part of the connector block, so the mysterious wire that 'should' go the terminal 1 isn't there.
Sounds about right.
The wiring centre looks untidy but is commensurate with many installations of that era. However, it would appear that the electrical connections look secure, the earth wires are sleeved, and there isn't any copper showing, so from an electrical point of view I wouldn't be worrying about it too much, believe me I have seen worse, much worse!
We have established that jumping L with T3 and T4 at the backing plate switches everything on and that by manipulating the room and cyl stat, the two channels switch on and off as expected.
Does this not tell us that fundamentally the basic components other than the timer are functional and given a hard wired (at the timer) 'all on' command, are working correctly.
Yes it does. It also means that the wires that are there do go to the right places.
I have a theory for you. I can't be sure, but it fits what is there, so here's what I suspect. Are you sitting comfortably? (showing my age now)..... Once upon a time, a system was installed with two, 2-port motorised valves. This type of installation doesn't require a connection to the programmer's terminal 1, so it wasn't installed. Later it was converted to have a 3-port valve. (often done at the time of a boiler replacement) Because the cylinder thermostat now needed an extra connection to the motorised valves grey wire, a slightly unusual T&E grey cable mentioned by @Harry Bloomfield, that was conveniently to hand was installed at the time. As it was far too much trouble to run an additional wire back to the programmer it wasn't done, and someone failed to set the programmer to its restricted settings (Gravity hot water / Pumped Central heating) which would have allowed the hot water to come on automatically when the heating was selected, thus allowing the motorised valve to get its live on the grey wire via the new wire from the cylinder thermostat..........After sometime, the systems present owner was informed about the missing wire and arranged to have it added, and they all lived happily ever after....The End
What next?
1) Replace the faulty programmer
2) Add the missing wire