Nick, that’s rubbish, that they can’t repair it. Did they say why? I am guessing there aren’t really spares for this diff as they don’t normally go. At least they have confirmed it’s the diff so any money spent will not now be wasted.
i would try 24/7part finder or another similar part finder, put in details and then an email is sent to all scrappies that are signed up. Hopefully you will get a better priced seconded hand unit.
if not here a couple of specialist Audi breakers to try
http://www.a8parts.co.uk/
http://vee-dubs.co.uk/
The following link is for a generic search as I mentioned, you might be lucky.
https://www.breakeryard.com/car-parts/audi
Best of luck. I guess I lost my 50p bet!!