Well done with the diagram MrGassafe. Back to the OP then. Here's a marked up wiring diagram showing a new programmer in place. I hope you can read it OK, the quality of the original wasn't great.
It would be best to remove the existing programmer plug and socket from the boiler terminals and wire the new programmer direct to the boiler in place of them. The control wires are shown in blue, but they are actually lives (I was running out of pen colours)
From the boiler terminals:
Connect Earth to new programmer earth terminal
Connect terminal L to the live supply to the new programmer
Connect terminal N to the neutral supply to the new programmer
Connect terminal 1 to the "hot water on" terminal on the new programmer (this operates the boiler gas valve via the thermostat)
Connect terminal 2 to the "central heating on" terminal on the new programmer (this operates the pump)
The link between terminal L and 1 should already be missing.
Use heat resistant wiring.
When choosing a programmer get one suitable for a gravity based hot water system that doesn't allow the central heating to be on without the hot water being on. (It's not crucial but it would mean that if you did select heating only, the pump will run, but the boiler won't fire up)
This assumes that the system hasn't been upgraded at some point in the past and converted to a fully pumped system with motorised valve(s)
Hope that helps, let us know how you get on, or if you need any more help after you have obtained your new programmer. Some programmers might require links across some of their terminals, depending on type.