I agree with oilman, but I think he meant do the test when the pump is running but the CH is OFF. Actually it would be worth doing while it's ON as well, for comparison. If the valve were stuck open all the time, then there would be heating all the time, which there isn't - depends how the programmer's wired ..
I don't think we've excluded the possibility of control coming from the boiler yet, though.
Just because the wire goes from the pump to the control box and not straight to the boiler doesn't mean the pump isn't controlled by the boiler, it's often just easier to connect things at a common point.
This point is easily resolved, either by
a) looking in the boiler to see if there's a PUMP connection, or
b) giving us the exact model designation of the boiler (as defined by GC number) so we can look it up.
Sounds like the odds are on the switch in the motorised head either being mechanically or electrically stuck. Annoyingly easy to check out if you're there and with a £5 multimeter - or even a 99p screwdriver, but tricky if not able to go into the electrics!
Many possiblities here - it depends how the programmer's wired too.