A shout-out is definitely due to Ian Bell and his website. This is where you can find the original source code for the BBC Micro version. Those original disks form the basis for all my Elite commentaries, including the NES project we're talking about here.
The core of the 1991 NES version (around 30% of the 128K ROM) is essentially the 1986 BBC Master version, which itself is a development of the original BBC Micro version from 1984. The Commodore 64 and Apple II versions are also cut from the same cloth (and they were developed on a BBC Micro, too).
Most of the code in banks 0, 1 and 2 is directly copied from the original BBC version, with a bit more in bank 7. There are new graphics, sound and controller routines bolted on the front, but the beating heart is still the Beeb version...
It was done by Christian Pinder: https://www.christianpinder.com/games/
People might also want to check out Ian Bell's Elite homepage, which has a number of the original versions:
http://www.ianbellelite.com/