It didn't register with me last night that you meant the TPS, until I saw the picture.

I did replace the TPS in the last year or so due to the erratic throttle response I was having, that Andrew was also experiencing, and since I've had the noise all along, that also rules that out.

But at least this has eliminated something else as the cause.

If you rev the engine in neutral, with car stopped, does it produce the noise? Just in case it is linked to throttle + speed

Have only been out in the car a couple of times, but did remember to try this both before and after a journey, and it doesn't produce the sound.

I checked every heat shield and they all seem secure enough, and also made sure everything else was secure.

I also have another suggestion worth considering. When I was out on Friday, I had the windows down to get some cool air in, and happened to drive along a stretch of road with a long wall next to it. To my surprise, I heard the odd noise being reflected off the wall (confirmed by easing off the pedal). Later on I was looking through ETKA for something, and came across an image which shows a bearing supporting the rear prop shaft. If this were worn, is it possible that this could be causing the noise?

Only thing is, I don't recall seeing anything like it when I was last under the car.

Hmm that is a viable culprit, and would normally be load related as the prop does move about a bit between acceleration and overrun. I've no experience of how Quattro behaves when that bearing is worn, but I do have an A4 prop in the workshop with a very loose rattly bearing so its definitely possible for them to fail like that.

IIRC you can't actually see the bearing on the D2 as it's hidden by the heat shields. To get to it you would need to remove the exhaust system and obviously the heat shields and then you can inspect and / or drop the prop. If the bearing is worn enough to be noisy its likely you'll be able to feel some play in it.

Typically Audi, you can't actually buy the bearing separately as the prop is balanced as an assembly and the bearing is non-trivial to change. People have found solutions for the smaller models, but I'm not sure about the D2. Its easier to just change the whole prop for a good used one.

That would explain why I didn't see it. Doesn't sound like an easy job just checking it, especially without access to a lift, so will have to think about it.