Houston, we have lift off....

...or that's what it sounds like.
UK E39 late 2000 post-facelift 520iSE Auto Saloon 72k miles
In the last few days, the auxiliary fan has become markedly louder. Not a
'bag-of-spanners I'm-just-about-to-shear' sound but a smooth '50,000rpm and cleared for takeoff' kind of noise. Easily audible from inside the cabin.
No visible 'shimmy' in the fan and on engine switch-off, you get a controlled slowdown and reduction in noise.
The aircon has been on 24/7 since the car was new.
I'm wondering if there's some accumulated crap in the fan well that's causing the noise. Can you get to it to clear it out without taking the bumper/fender off?
Any other advice greatly received.

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