I get pretty strong gas fumes only after filling the tank and they don't last very long. It's as if there is a small splash somewhere that evaporates. Any thoughts or advice on what might be the cause will be appreciated.
I read somewhere that the tank is under the rear seat and gaskets can be replaced fairly easily. Is this the case? If so, I might consider looking at it myself. If I have to get under the car then I will hire the work to be done. I just don't do that anymore.

 

Dennis the rear seat does cover the tank and its pumps. There are 2 tabs that you slide one way or the other that release the front of the rear seat, pull up and out, remove the 2 body covers to reveal the pumps. You only need the two tangs on the lower seat portion.

 

Just another comment.
I see you also have a 2005. There was only one safety recall for the 2005 S Type and it was the gas tank. Mine was completely replaced by the dealer.

Call Jaguar and verify your car has been done. Note that very rarely it has been reported that the gas smell came back even after replacing the tank.

But do check because since it was a recall you have a chance of getting fixed by Jaguar. This is a maybe because in the US it looks like there is a 10 year time window for doing safety recalls and we are now in 2015.
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I called the Jaguar dealer and no open recall for the car and the service guy seems to think it might just be some spillage at the neck when it was filled up seeing that the smell did not last long. I hope he is right but if not, I appreciate the pictures and advice.