The other thing that makes a TD5 fuel pump NOISY is GAS in the fuel.
(Most of the noise actually comes from the stupid fuel filter in the right rear wheel-arch)
If there is ANY gas leaking past an injector copper washer, which is a common problem with a TD5, several bad things can happen, like a noisy fuel pump, poor starting or NOT starting, and rough running. This fault will not show up on the dash display.
You can test for this - turn the key till the dash lights come on but do NOT start the engine. The pump should start, and for a second or two it might be a bit squealy-cat sloshy noise, but it should suddenly run smoothly, no squeals or sloshes.
The pump should run for a couple of minutes then stop.
Turn the key OFF, then ON and start the engine. Let it tick over for a minute or two.
Now stop the engine. then turn the key ON but don't start the engine.
If the pump noise is squealy sloshy again, chances are there's GAS getting into the fuel system.
However, the FIRST thing to do with a TD5 is to fit a clean FUEL FILTER, taking great care when you change it that you take TWO O-rings off with the filter. The TD5 has a very bad habit of leaving the small O-ring on the filter head, where you won't notice it. Everyone who changes a TD5 fuel filter should make sure next time they do it that there isn't an old O-ring trapped on the filter-head. It needs ONE big O-ring and ONE small one.