Having pulled together all I can find from various sources, I come to the following.
Corrections/additions appreciated.
N.B. this purely considers Timetable data, not live arrivals/predictions (perhaps another thread).
Most comprehensive and accurate, and AIUI, the root of all LU timetable data, is the signalling control timetable. This uses ‘seconds since midnight’ timings. [not publicly available]
From that directly came the now-obsolete CUF CSV files (http://timetables.data.tfl.gov.uk/). You can see they also use(d) 5-digit timings. [current data not publicly available]
WTTs and TTNs (which replace/superceed portions of WTT for periods to cover e.g. seasonal variations and engineering works in progress) are derived from the same root source, but timings are transformed to hh:mm quarter-minute accuracy. [latest WTTs publically available from Working Timetables (WTT) - Transport for London in PDF only; TTNs not publicly available]
There is timetable data available from the TfL Unified API https://api.tfl.gov.uk/Line/{id}/Timetable/{fromStopPointId} [publicly available]
That has timings reduced to minute accuracy and attributes such as TrainNo/TripNo being dropped. Also, the Interval data (time from one stop to another), has been standardised and simplified.
I suspect, but not certain, the xml data from https://tfl.gov.uk/tfl/syndication/feeds/journey-planner-timetables.zip is a superset of the API Timetable data, but with the same limitations. [publicly available]
