Thanks Gp79 - that's a pretty comprehensive set of instructions!
Catman, I tried it again this evening, and you're right. The cc light is flashing. That combined with the lack of priming noise feels fairly conclusive?
So as a start just for confirmation I'll connect 12v direct to the pump and see if it will run. If it does then I guess this suggests a relay fault? If it doesn't then its probably the pump?
Assuming it doesn't work with the 12v, then then I order the Alfa Relay, Alfa F1 Pump, the transmission fluid and wait for a day which looks like it'll stay dry (I have no garage).
Pretty nervous to be honest. I've messed about with a few cars before..... but never one that's actually worth anything!
Wish me luck!