Originally Posted by Jordo!

High pitched whine or metal-on-metal?

If the former, it's something electrical -- there used to be a known issue with "ECU whine".

There is also an occasional fuel pump whine that can be heard when shutting the car down -- it's possible that something is amiss with the pump or the switch for it. I can't recall the exact reason for the noise, but its worth checking.

If it's metal-on-metal, the brake dust shield can make contact with the caliper and cause a horrendous metal on metal screeching noise.

On inspection, nothing will be apparent and it doesn't even seem to cause any visible scoring or damage. Basically, the shield just has to be bent back a bit for a few mm of extra clearance.

Can you post a recording of the sound?