The screen washers are not working. Just a little dribble at the driver's wiper.
The pump is working. Are there any usual suspect areas/hoses to look at?

 

Yes the pump sits at the bottom of the tank and can become clogged.

Remove pump-just pull it out and clear debris but you will lose all fluid in the

tank. The pump is just a push fit into a rubber seal.

Remove wheel arch to access tank

 

Check the rubber hoses at the base of the arm at the attachment point to the pivot. Remove the hose connecting to the arm at the base of the windshield, and then apply washer. If you see fluid coming out then move to the arm itself. Remove the nut, remove arm and invert the arm assembly and check to make sure the hose isn't pinched in the spring or the spring pin.

 

I second the possibility of a gunged up tank, I have had that problem on my past and my current X350

 

Is it an easy process to remove the wheel arch?

 

turning the wheel when on a stands/lift will give easier access to the screws

another thing i did was to take a needle and clear the passages of the "nozzles" themselves

edit: although i guess you dont need to have the car in the air to turn the wheel

 

Most washer pumps these days have a little plastic mesh filter, which clogs up badly with sludgy soap residue. make sure you clean the filter as well as the pump.

 

I made this thread -
https://www.jaguarforums.com/forum/x...sy-fix-182039/

Also make sure the lines to the washer nozzles aren't getting pinched by the wiper arms and restricting flow.

 

I followed your method and unclogged the lines using one of those air in a can dusters. Large gush of washer fluid erupted!
I changed the cabin air filter as well. It was dirty with lots of leaves and dust at the bottom outside of the filter holder.
I will clean out the pump filter at some stage.
Sooner rather than later, the rubber boots on the upper control arms have rotted away!