Fuel Level Sensor / Sender Fault?

[amac01]

When the electrics are on, the fuel gauge indicates full regardless of how much fuel is in the tank (the dial returns to zero when the electrics are off). It has done this now since I first filled up after buying the car (it took a few days to twig that it was faulty). The miles to next fill up keeps increasing so I guess that means it's a fault with fuel level sensor or sender and not the gauge itself?

I would be grateful for any advice about how to confirm what is faulty and what to do about repairing it. Also, as the car is just out of warranty (<2 weeks), do Seat ever sort problems out of good when the warranty has just expired?

Seat Alhambra Stylance 2.0TDi 06