1047752 is the finis number of the heater valve from Ford. Is normally only about £30 (so not THAT dear).

IT almost certainly WILL be the fault. What happens is that there is a plunger solenoid inside the valve assembly which over time gums up. Disconnecting the valve will be of no use.

In the 3 1/2 years that I ran the Trade Parts Sales Dept of my Ford dealer, out of the 300+ valves we sold a year, we sold maybe 3 control units, and out of those 3, only 1 person didn't try to send it back for a control valve.