The electric fuel pump in the Jaguar XJ-S sometimes gets noisy, noisy enough that the owner takes notice.  Often, this is the result of an obstruction in the pickup, and it is of the utmost importance that the owner investigate immediately and make sure that the pickup screen is unobstructed.  If the car still has the early design pickup screen, it should be replaced with the later type that is far more difficult to plug up -- or, alternatively, the pickup screen should be removed altogether and an inline filter installed in the suction line to the pump.  Failure to address an obstructed fuel pickup situation can cause the engine to run lean at high power situations, which in turn will result in burned pistons.

If you're lucky, though, the fuel pump noise is from a far more innocuous cause.  The pump is mounted in foam that it intended to isolate the vibrations of the pump from the car.  However, the pump tends to slide downward until the hose on the outlet fitting on the pump is jammed against the floor of the trunk.  The isolation is thus defeated, and the sound the pump makes is transmitted through the metal of the car.  Looking at the arrangement in Kirby Palm's '83, you can see how this happens:

Note: Palm's car has a metal fuel line fitted, but most cars just have the hose continuing on to the main filter.

The pump is cylindrical, and is prevented from sliding downward only by friction.  There is a ridge around the outside of the pump, but it is located underneath the foam and therefore prevents the pump from sliding upward.  This is a picture of Kirby Palm's pump in its mount:

The ridge is actually supposed to be up against the bottom edge of the foam; the fact that it's not indicates that sliding has been going on.

Palm's idea for a fix is to clamp something around the pump on the other end of the pump to keep it from sliding downward.  It needs to prevent the sliding while still isolating the pump vibrations from the rest of the car.  What he ended up doing was to wrap a layer of 1-1/4" x 1/4" foam sealing strip around the pump, and then clamping it securely in place with a worm-screw clamp.  The clamp can be located around the upward edge of this foam strip so that it doesn't contact the bracket.  The assembly looks like this:

By the way, if you look closely at this pump you will notice that both terminals have the same size spade.  This is a replacement pump; on the original, one spade is larger than the other to prevent mix-ups.