Ok LB. I just wanted to rule out anything to do with the shower.
It does have all the symptoms of a problem with a "soil stack".
The other posters have referred to it already.
A soil stack is a vertical 110mm pipe connecting the drain at the bottom to the flats above it. It's where all the poo etc goes down to the outside drain.
Since you mention a bung up in the garden manhole, it would suggest a blockage (maybe partial) somewhere in the stack.
Burbling and glugging would result.
Upstairs' constant overflow drip might well be the dripping you hear 24/7. Perhaps you could ask upstairs to flush while you stand in the bathroom and listen. My thinking is that, if you can hear the dripping, then you should be able to hear the flush coming down.
My problem is that you say the noise is behind the shower. It is unlikely that a stack would be positioned there (you wouldn't be able to fit the bath around it.)
Possibly the stack is within the wall behind the shower.
Anyway, I would be very surprised if it has anything to do with the boiler. Just coincidence.
I think I would rod the whole stack to investigate. Anything could bung it up, J-cloths, wet-wipes, nappies etc.
If we are right, and it is a stack, then I should explain that they normally run up through every floor, picking up waste from each flat.
Anyway. I think further investigation is needed (rodding and generally poking around.)
Of course, it may be something else entirely, but this would fit the bill.