There are also silencing kits available for the box itself. Alloy boxes tend to be quieter, as aluminium is a fairly dead material compared to sheet metals.
I used to get a buzzing from my box as it stands on a wooden desk. In fact the buzzing was caused by resonance through the desk. Moving the box slightly made a lot of difference.
Common fault with the wiring is that the plugs which go into the back of the box are not strong enough to support the weight of the wiring. Over time with alternate hot summers/cold winters the plastic plugs will work their way loose and at a certain moment cause arcing with the pins in the power supply so it's a good idea to support the weight of the wiring so that it isn't pulling downwards on the plug(s).
Just one of the common ways of losing the Power Supply Unit.
You mentioned some B&Q self adhesive cable ties Sandra, are they strong enough for this job?