Ok, so I replaced the aux belt and tensioner which was noisy and I'm pretty sure its not the alternator.

My question is, what would create this whirring noise, its temperamental, I can start the car up and it'll make this noise other times it won't, doesn't seem to matter if its hot or cold.

I'm wondering if its a potential bearing failure on the shaft that leads to the alternator or a turbo failure. Definitely hear it at idle and on the move.

I have a 1.8 TDCi Mk2 Focus (56 plate - Jan 2007 production)

Any ideas?

Just to make sure there is no confusion with the bearing on the alternator; the aux belt drives a shaft which then links on to the alternator which is independent to the alternator.

Could be the water pump. We had it on the SportKA. Some days it was ok, then it got worse and eventually the noise was so bad I had to take it in. I thought it was just the auxilliary belt tensioner as that is a common issue on these, but it was the water pump siezing.