I had quite a detailed conversation with Grant Showbiz about his producering work on Rank, once.
I had assumed that it was just a nice soundboard recording, but each of the mics and instruments were recorded separately by the BBC. Grant mixed it in the studio, presumably the same studio that he mixed Girlfriend in a Coma. He told me that for a lot of commercially released live albums bands would re-record parts that they weren't happy with, but everything on Rank was from that gig.
When it was broadcast by the BBC it included more songs than Rank, including quite a fancy version of How Soon Is Now. Worth a listen.
I used to live between Maida Vale, where they did their Peel Sessions and Kilburn where they recorded this. The former is a
very posh neighbourhood, the latter
was pretty rough. Or at least it was when I lived there; seems a bit more gentrified now.