Good news and bad news. The good news is that I got it back last Thursday and it was great, just as I had hoped it would be. The bad news? It broke down again yesterday morning, huge lack of power, intermittently, which is the same root symptom as before. So I called VW Assistance again and got them to take me to the dealer for a meeting. The car was taken to the dealer later.
I've told them I have no confidence in that car, or in their ability to fix it. Was it the ECU? I don't think so, I don't really think they fail like that. It's done < 700 miles and broken down three times! So I am waiting to hear the dealer's proposal to me. I would like a GTI, as I said at the beginning, it was a great car, and I don't know what else I would buy, but on the other hand I've had a pretty bad experience both of the dealer and VW.
Amusingly, the customer services person from VW who had been dealing with me rang, I think to check how things were once the car had been fixed. That was at the exact time I walked into the dealer, the car having failed again! Needless to say she was somewhat shocked.
I will keep you all posted.