I think I've digested what you've said now, so here goes.
Firstly, for your CH you are ostensibly going to be ignoring the
original programmer completely (you'll need to set the CH programming on it to permanently off). So for the purposes of this discussion it is not going to be used. In fact from the looks of the backplate wiring, it was only using that one channel anyway for CH (maybe just to enable your cleansing cycle to run?) and not using the HW channel at all.
So for your temporary bypass, you can take your live feed to the
new programmer from the third terminal down on the boiler connector(L) OR more correctly, link down from terminal 3 to terminal 7 and take the live feed from terminal 7 (connected to com in the new programmer).
On some programmers a link is needed from com to NC (that doesn't appear to be needed here for the horstmann though).
I'm
assuming that the boiler connection (switched live) has been placed into the right hand side of terminal three currently. If correct you'll need to move that to terminal 8 (right hand side) and connect the core from NO on the stat to the left hand side of that terminal (enabling the stat and built in timer to control the boiler).
IF that's not what's been done then I can't tell from the picture what's controlling the boiler.
If that was correct then you'll just need to wire the pump and any valve in to terminal 8 to control them.