Cliff,
I haven't quite given up on this, but I am running out of leads. I'm dropping this here mostly to benefit others by leaving some information all in one place.
It seems that it was first episode of the first season [S01E01] of a Yorkshire Television series named Science Fiction (oh, how I wished they'd picked a less-ambiguous name). This episode was named Spycatcher.
It's listed on IMDB[0] with an air date of Feb 15, 1990, but that date may be wrong. It was discussed twice[1] in TV-section articles in the Hull Daily Mail (Feb 10th and 13th, 1990), and some freely-visible blurbs from those suggest that it aired on a Tuesday at 7:30PM. That more-strongly ties the date down at February 13, 1990 than the IMDB's entry of Feb 15th.
Except: The verdict in Germany didn't come until Feb 15th[2]. I wonder of the Yorkshire Television Science Fiction episode had the same conclusion as the PBS Nova episode did, or if it left things more open-ended. That would help to pin down the date. :)
Some of the clues along the way include an old copy[3] of your own web pages at Berkeley, and one comment[4] on HN from a couple of years ago (they gave up on finding it).
I don't know enough about British television norms (much less the history) to really understand how any of this stuff flows, but I'm gaining the impression that the remains of Yorkshire Television might be owned by ITV, and that archives are likely to still exist.
I've seen reports that people have had success purchasing personal-use copies of old programs by sending an email to viewers.requests@itv.com if anyone wants to go that route.
[0]: https://www.imdb.com/title/tt1385328/
[1]: https://www.britishnewspaperarchive.com/search-newspapers/re...
[2]: You're mentioned in a world record by Guinness! :) https://www.guinnessworldrecords.com/world-records/612868-fi...
[3]: https://web.archive.org/web/20090415204255/http://www.ocf.be...
[4]: https://news.ycombinator.com/item?id=39154781