wouldn't the 10M MPP of current GPS be good enough for "where is the 19.23 from Paddington?"
are you sure that is what it is used for?
a train typically works with a platform clearance of 15mm so they are a tad more precise nowadays than back in the steam era.
on mine sites they use augmentation to give half millimetre precision I'm told which allows for all sorts of automated positioning.
automated braking to stops would be facilitated by really precise position information. (of course not in underground stations.)
anti collision systems would be another use I would think.
power supply switching on electric rail another.