Here is an odd question..

I wonder if there is some sort of 'overheat' safety trip-out on the X300 air conditioning ?

Yesterday it was 26'C at lunchtime here, I got in my car which had been in the sun all morning and was an oven.. but the aircon was working well within a minute, even at slow urban road speeds.
Then today after work, same scenario, but it was 27'C. The air con seemed broken the whole way on a 15 mile trip home, even at speeds of 100km/h with plenty of airflow across the radiators. I thought I was in for a big repair job.
Then an hour later I fired up the car to move it into the driveway and she was blowin' cool again..

In the past it has worked fine, even in local temps up to 32'C

 

Actually it has safety cut out controlled by trinary switch near the right bulkhead, if the pressure is under 2 / over 20 bar, the switch is cut off and stop the compressor.
The AC system has a self diagnostic system, so you can check the error code by yourself.
Here is the page which shows how to do it;

JagRepair.com - Jaguar Repair Information Resource

Referring 14-10, check the 2 digits "panel code"