There’s an Audi main dealer in Chingford, it’ll be pricey though. There’s also autodeutsche in Camden not *too* far from you who are about 10-20% cheaper than main dealer prices IMO.
I’ve been looking for someone independent, local and Audi-aware in the same/similar area but no luck so far.
To replace the tailgate entire will be a really big job. If it's just the glass that's broken, a windscreen fitter could cut the replacement glass out and fit it to your existing one. The other bit you can swap in situ is the lower panel where the number plate sits.