Whistling noise, part identification help

[Rob13]

The 5 has developed a very annoying whistle, particularly loud upon startup but once its warmed up, it can still be heard faintly and intermittently.

I think ive narrowed it down to part central to the belts. If looking at the belts front on, its not the alternator on the left, nor is it the pump on the right but appears to be coming from the middle pulley. What is that? The belts have been off and lubricated but it hasnt made a difference.

Can someone help?

[Rob13]

Can the belt not be slack and need tensioning?

If its a new water pump & cambelt, ill cry. Ive spent hundreds on service, and getting it through the MOT, booked in for the arches and wheels getting done next month just to get it sold.

[Rob13]

The garage said they had taken them off (didnt charge me) but I suspect they just sprayed the belt. How are they tensioned up? Is there a measure and can it be a DIY job?