Fixed!!! And as I expected, it was simply the fuse..
I'd been working off online fuse charts and they don't match mine 100% (for some strange reason).
Fuse box Audi A3 8P (fusesdiagram.com)
I ended up buying a new multimeter (another excuse as mine was 20 years old!) and the Fluke accessories, which came with some nicer 'probes' that were handy. I just plug one end in to the unplugged 'connector' at top of the fuel pump and the other end I just started to probe in the engine fuse box... it got a signal on F7, which had no fuse..
Obviously I'd remove that one when I was trying to fault find the horn problem (and dropped it in to the engine ether!).. then plugged a spare on in to the wrong slot, based on the pic from the link attached.
Anyway, all done now, and I have a new fuel pump (higher rated!) and new adapter coming that will be spare
I'd love to actually get a proper map of what the fuses are in my car, but everything seems to be working fine (except the boot light), so I might try the same logic on that one to see if I can work out why it is not working as well.
Thanks all for all your help, it was great to reach out to the community again and get support when you need it, and all for free
