The S type workshop manual has a whole section for removing the EPB motor including easy to follow instructions and diagrams.
It can be done according to the manual by lowering the DIF and leaving the subframe alone. Whether that is workable in practise?

 

OP, like it's been suggested you can release the parking brake if the fault is upstream of the cable motor. BlackKat gave description and here is youtube link to illustrate:
I've gone through this myself and now suspecting the PB module in the trunk to be at fault. Based on Jon's experience it seems new module and reprogramming at a Jaguar dealer is what's needed.

 

I'm not sure but I expect a used module with the right part # would work and also not require reprogramming. (If it's the module at fault.)