Not sure if anyone else is following this but here's an update.
I've managed to finally remove the compressor/pump - following a write up which a previous member wrote on this forum, available
here - many thanks to Glyn.
The write up makes more sense once you've done the job (if that makes sense), it's a little hard to do, but I managed it okay and i'm no mechanic!
Anyway, whilst the compressor was on the car I did try to actuate it by putting a +12V feed to it from a motorbike battery, and also the ground, but had no luck.
So just as I had put everything away (it had gone dark!), I wanted to settle my curiosity - I took the battery again and put the feed to the compressor; this is done by using the lowest of the three connectors. And what do you know?? the thing comes to life and starts choo choo-ing like a little train.
So; this means that the compressor is good. What does come to mind is that one of the VCDS scan errors mentioned something about shutting the compressor down due to something, so I wonder if the reason why it didn't actuate when I gave it the feed, whilst on the car was because it had the other two connectors still connected? in other words there is some condition which is causing it not to come on?
anyway, I'm still learning and quite puzzled.
Hope this has helped someone, and if anyone cares to explain this a little more, I for one am all ears!