I currently have a similar problem, the first time the 'Low Fuel Alert' message appeared was about 5 miles after filling up the tank. For about the next week the alert appeared and disappeared intermittently, before becoming a permanent alert. I had the car booked in with the local Jaguar dealer to look at this and a number of other alerts that all appeared within days of it being serviced (by a Jaguar garage), but before the appointment date things got worse with the engine juddering every few seconds and cutting out at idle and slow speeds. Unable to drive it to the Jaguar dealer I took to my nearest independent garage. They had a look and told me that the fuel level sender float was sticking, and if the computer thinks fuel level is too low it stops the engine to prevent damage to the injectors and various other components, which running the tank dry would cause. The local garage told me it will probably still need replacing, but there is a 'get home' solution. The fuel level sender unit is underneath the offside rear passenger seat, with the seat removed if you give the unit a tap it frees the float (hopefully, unless its really stuck fast) fuel level indication returns to normal and away you go, until it sticks again. I haven't looked at whether the sender unit is a DIY replaceable item as there are still all the other alerts that I need the Jaguar people to resolve.
