Simple trial and error with
www.nationalrail.com; starting with your initial lucky discovery and using a straddle-and-close-in approach to find the date. Tried a few more nearby origins and worked out... also to journeys with fares set by other operators.
So far, the most extreme example of "vaguely via London" I have tried that works is Trowbridge-York (which for some reason also works via Bristol, in addition to via London)... and an "anytime" return suddenly becomes super-off-peak (one month validity).
It beats doing Sudoku.