The correct leads does exist. I came across a video while looking for the best solution for hooking up BT for my B6 A4 with Bose. I was looking at a lot of semi-relevant videos, but there was one from Enfig in the states that showed an aftermarket radio coming on without ignition, steering wheel controls, dash integration, the lot. I think the lead was around $99 though, so not exactly cheap. But it does do exactly what you would want, so the ability to do it is there.Here is a video I found. I have started it from where he shows the aftermarket stereo turning on and doing it's thing. He then goes on to show how it stays on even after the ignition is turned off.
The adapter he uses is this one:
https://enfigcarstereo.com/ENFIG_SRWH_AUD2_HILO.html
Not sure if there will be a UK supplier, or how much it might cost or whatever. But for proper aftermarket integration, that looks like the way to go. If I'm sitting for any length of time though in the car, I usually just listen on my phone, so my battery doesn't drain and I cant start the car (this happened once). But then I'm usually listening to Radio 4 or Scotland, so generally just chat. So don't really need it pumping through my speakers. I do that to save spending $99 or whatever on an adapter that allows me to do otherwise.