Today my car (2001 1.2 16v) overheated but the red temperature light did not come on and the needle on the gauge was almost at the top; the fan did not run.
Does the light use the same engine sensor as the gauge?

yes. the light comes on when the gauge hits red (110degrees AFAIK)

if the fan didn't come on check the fuses for it, I think the fan fuse is actually under the bonnet instead of inside the car (look in manual it tells you where).
if the fuse is OK and the fuse socket isn't burn't or melted atall then look for the fan relay and check that is OK.
if both are OK, then you need to maybe replace the fan 'stat its somewhere screwed into the back of the radiator. you'll need to ask for advise to check/change that

.. no "switches" or "stats" on the rad, the fan motor is confirmed knackered. I have taken it apart and the culprit seems to be the rear-most bearing. Now I have a choice of buying a new or second-hand one, repairing this one or fit something more substantial.

I do not think later models have a temp. sensor in radiator (older cars pre 98 ?
do). Post 2000 cars use the ECU to turn the fan on , and I believe the temp sensor for this is in the block on the heater outlet just behind coils. There is a green temp sensor there on my car a 2000 Punto 1.2. Can any one confirm
Thanks

Your right, they don't.
With my new (secondhand) Alfa 75 fan fitted, it works great. The motor fits up correctly but needs to be mounted "behind" the radiator shroud and a bit of "bodgery" with the fan is required. The gauge registers just over half for it to activate.

Mine comes on for about 10 minutes and then disappears, is this something i should worry about? I have just had the coil pack replaced.

In normal driving it does not run but in very heavy traffic, it runs for about 30 seconds in this (cold) weather. I have no idea how long it is supposed to run for but 10 minutes does appear excessive.