The servo is #4 in this illustration

Air Conditioning Components - Parts For Series III Saloon | Jaguar Heritage Parts UK

Cheers
DD

 

have you checked the check valve shown in the following picture above the yellow arrow?

 

Those 2 vacuum switches, no.5 in Dougs pic, are the ones for the center vent and water valve. They are controlled by the cam in the servo.. Sometimes they are broken or plugged. Often the red and black lines from those switches have become disconnected. Check them at the servo.
At full cool 65 deg, the water valve should close by the vacuum from the red line.
You can see these valves working when the servo does its thing..You can see the end of these switches with servo in situ.