Welcome James,
If all the ducks aren’t in a row for DVLA, then they will run you ragged - as you are now finding out!
Not wishing to make things worse, but expect to find another hurdle close down the line once you eventually sorted this out!
I dealt with them in a capacity of ‘DVLA Adviser’ for a Classic car club for a couple of decades prior to Covid, and I understand it’s a lot worse now.
My advice was to never to buy a car without paperwork - too late for you!
Can I take it the car has an original legible VIN plate securely attached with original fixings? If so, you should eventually get a reg. no. If it doesn’t then you can kiss goodbye to any chance of a reasonable rough paths to success.
Build record/ year of manufacture? Simple route first - go along ( don’t phone) to your local Audi dealer armed with VIN and talk with the Parts Dept. Long shot chance, but eliminate it.
Join a German Audi ‘classic car’ club, and get them on board to deal with Audi Germany for you. They are more likely to get some degree of success than you are.
Approach FBHVC and seek their advice. They can act with advice and liaison with DVLA - probably at a price.
Some possible avenues to go down, so please let us know how you get on.
One thing to bear in mind is, when DVLA closed their LVL offices, such matters were handed over to the Kit and Rebuild Section at DVLA, so you can guess the logic of treating any unknown as being a ‘ bitser’.
Regards,
Gareth.