Changing the engine rpm sensor cured it. £35 for the part from Alfa dealership in Northampton. For the benefit of anyone with a similar problem, here's how I replaced the sensor.
Vehicle: 2002 1.6L Alfa 147 (103HP version)
1. Buy the elearn workshop manual of Ebay!!! My copy cost £2.99
2. Disconnect the Battery negative, and the electrical connections for the lambda sensor and rpm sensor (white and orange clips respectively) near the injectors.
3. Remove the heatshielding that covers the exhaust manifold and catalyst (4 bolts)
4. Disconnect the 2 electrical connections for the lambda sensors in the catalysts
5. Split the exhaust system at the point just upstream of the main silencer by removing the 2 bolts holding the exhaust together and the 2 bolts holding the exhaust to the chassis.
6. Unhook the downstream lambda sensor cable from the chassis (enough that the exhaust can reach the floor without the cable taking any weight
7. Remove the bolt for the remaining flexible mount on the upstream section of the exhaust
remove the long horizontal bolt holding the catalysts to the lower part of the crankcase.
8. Remove the 5 bolts (3 from above, 2 from below) holding the catalysts to the exhaust manifold)
9. Gently lower the catalysts and the front half of the entire exhaust away from the vehicle
10. Reach up behind the sump into the gap you've just created to remove the single bolt holding the black plastic rpm sensor into the crankcase (Allen key head)
11. Remove the rpm sensor making sure to remove the rubber o-ring that will probably get stuck in the recess.
12. Lubricate the the new rpm sensor with some clean oil and refit using the allen headed bolt.
13. Take the old sensor cables out of the clips leading it to the top of the engine and feed the new sensor cable through these clips instead
13. Refit: the catalyst (5 bolts), the long horizontal bolt, the first flexible mount, the second flexible mount and the two sections of the exhaust. Restrap the downstream lambda sensor cable through its clips so its not hanging down.
13. Reconnect the electrical connections for the lambda sensors (3) and the rpm sensor.
14. Bolt the heat shielding back over the catalyst.
15. Reconnect the battery
Took me (a rookie!) about two hours to do this. Probably takes about half that if you had done it before.
Thanks to Smaky, Ronan and David C for the diagnosis. Much appreciated.