I recently noticed a new noise from 'the engine'. An extra whirring noise that is linked to engine speed which tends to be there for a little while after startup but goes away. Today I found that it stops immediately if the A/c button is pushed (to switch it off) and returns immediately when switched back on again. I therefore suspect either the compressor or the clutch. The a/c is still blowing cold when expected. Any thoughts/experience?

Doesn't have a clutch but will be under more load when cooling (it never switches off). I'd pop the belt off and double check the noise has gone with no belt, then have a feel of the tensioner, alternator and compressor for anything obvious.

Are we talking about it being noticeable when driving at normal speeds or stationary with window down frinstance?.

Noticeable at slow speed (in a car park fr'instance) from inside the car, windows up. Like a noisy bearing or something.

I wonder if the compressor has enough oil?

I guess the button activate the fan also which I find is the most noticeable noise in an enclosed space but it should be possible to analyse it with the bonnet up in the open I would have thought.

I'm certain it's not a fan noise, as the correlation between activation and noise is immediate.

There must be some mechanism that enables and disables the a/c, thus changing the load on the compressor.

The variation of internal capacity flowing through the compressor is what changes the impact of load on the engine, as techie has already said - it never truly turns off, it reverts to 2% activity to keep mechanical components moving and refrigerant flowing.