The noise rises and falls with the engine, so is not the fan. This noise is also typical of a bearing failing, and is unlikely to be internal to the engine.
Possible causes:
Alternator (Quite likely)
Aircon pump if fitted (least likely)
Water pump
Cambelt tensioner (Likely, but they usually sing a slightly higher note)
Clutch release bearing (Quite likely)
Gearbox shaft bearings (Possible, and disappointingly expensive)
Determine if the noise is at the front of the engine or the rear. Front is at the timing belt, rear is at the gearbox.
Front: Remove the auxiliary belt to rule out, or in, the alternator or aircon. If noise still at the front, needs a cambelt, tensioner and water pump, always do the lot together.
Rear: Does the noise go away or change if the clutch is depressed. If it changes with the clutch depressed, it is most likely the clutch release bearing. Replace the whole clutch, using a good brand such as Valeo or LUK, don't save money here, doing the job twice is not clever.
Check the gearbox oil level. If it is ok, the bearings are likely to be ok. Is there, has there been any leaks from the gearbox? All leaks will stop if left unattended, when the vital fluid is all gone.
