One of the many things that is awful about the TV version of “The Hitchhiker’s Guide to the Galaxy” is Trillian’s screechy voice. Trillian is supposed to be an intelligent character but this voice of hers just made her sound stupid.
I dismissed this as yet another of the BBC’s failings with the TV series and forgot about it.

A few years after having noticed this, I bought the DVD set of the series and watched the many “making of” extras. At one point, they showed a recording session with Douglas Adams and an actress whose name I didn’t bother to remember:
Actress whose name I didn’t bother to remember: “What accent should I use?”
Adams: “American”
And then I heard something similar to Trillian’s screechy voice!

The penny finally dropped – Trillian’s screechy voice is what these folks thought was a passable American accent.

This means that Trillian’s screechy voice is still a failing of the BBC but from a direction that I hadn’t considered.