The issue manifests as a fuel gauge that either doesn't register any change past a certin point or keeps dropping to zero. From my investigation it appears that the root cause in my case was a "sticky" fuel sender float. I have read in a few other forums that Jaguar are also aware of an issue with corroded connectors within the sender pump assembly but I couldn't see any evidence of this issue on mine. If you are not sure have a look at the recalls for the 08, 58, 09, 59 models.
So here's what I did.
1) Removed the rear seat (two catches under front lip)
2) Remove the rear step trim on the rear door edges (flat logo'd bit lifts up then who piece slides towards front or car
3) Pull back carpet both sides
4) Behind the drivers side (UK) you will find a black rubber hatch (size of a dinner plate) - pop this out
5) You are now looking at the back of the fuel pump and sender fitted into the top of the fuel tank
6) Disconnect the one black electrical connector
7) Disconnect the two fuel lines (push connectors each side) and had a small cup to catch any excess diesel that may drip out

9) Carefully lift out the top unit (you will see into the tank) (Always advisable to do this a as low a fuel level as possible)
10) With rubber gloves on put your hand in the tank and move the fuel sender float right across the movement spectrum ie: back and forth a number of times to ensure it can move freely.
Once done, reverse the process and reassemble.
As soon as this was done, I had a fully working gauge. I went and added fuel and immediately got a reading. I will keep an eye on it now and report back but all looks good.
Given I had various quotes from £150 to £800 to fix this, I would strongly suggest you give this a go first before paying out. I only wish someone had written this for me before I found it out through trial and error.
Hope this helps one of my fellow Jaguar enthusiasts out. And should you need to ask any questions, feel free to mail me on marc@jolly-web.co.uk.
Regards
Marc