12/6/82 Hammersmith Palais is a classic BBC recording, yes.
There are a few different BBC radio promo CDs featuring tracks from this show, none of which contain the full concert, as far as I know. Most, if not all of the BBC CDs contain only five tracks from the show, and I think that between them all, they only cover 8 or 9 of the songs in total.
That said, there are a couple of BBC-produced vinyls that contain the full show, and the best bootleg in circulation is taken from a 1st-gen recording of the radio broadcast, but a digital radio copy would likely be better than any of those!
The most well-known bootleg goes by the title "An Electric Company on Stage", by the way. Great show, great sound.
There *are*, however, some Westwood One Radio promo CDs that do contain the whole show (In Concert #99-47; In the Zone #00-07; Superstar Concert Series #02-09; Absolutely Live In the Zone #02-22). Not sure if any copies of these have been put into circulation.
Bottom line, I don't think anyone would complain if a copy was made of the complete digital radio broadcast, provided one clearly indicated the lineage/method of the recording.