There are some practicalities in the way timetables are / were presented.
You get some trains which operationally are a single journey from A to D, but may appear in public timetables as a journey from A to B, another journey from B to C, and another journey from C to D.
Depending on which public timetables are combined at any one time (it does vary) and how train operators choose to schedule trains, you could count it as one journey or three, but what's actually on offer to the public isn't much different.
Similarly, one train journey might appear in two timetables, for example on the Dartford lines out of Charing Cross, at some times the whole lot has been presented as one timetable, at other times as three for the different routes - when it has been the latter, maybe the timetable for the line via Woolwich would show all trains going as far east as Gillingham, the other lines would only show stations as far as Dartford, so a train to Gillingham via Sidcup would appear in both timetables with a note in the first to say it's via Sidcup, and in the second to say it continues to / from Gillingham.
Then there are 'circular' train journeys, again an example from from the same patch, there are trains that run from Charing Cross or Cannon Street to Barnehurst, then go 'round the corner' to Crayford and back to a London terminus. In the public timetable it's shown as a down train on the Bexleyheath line and an up train on the Sidcup line. Operationally, at some times it's been regarded as two separate journeys, either running empty or in passenger service on the connecting move. More recently it's tended to be regarded as a Cannon Street to Cannon Street journey.
Then there's branch lines that used to have through trains but now run as a shuttle - possibly the overall number of train departures per day has increased without much change to the level of service anywhere.
And what about trains that divide / attach somewhere on route, so that it's (for example) one departure from Waterloo then two departures from Woking - does that count as one, two or three train services? Or one from Waterloo, but two separate departures to Waterloo?
There must be a heck of a lot of examples like this.
I'm not sure what counting the total number of 'passenger trains' per day would prove, quite apart from the time it would take to go through a doorstep sized 'all lines' timetable to count them.
The number of departures per day from specific stations, or on specific lines, might be a useful comparison, but I can't quite see what it proves on a national basis.
I'm not sure I've seen the figure quoted until quite recently (for example South Eastern are quoting the number of services per day / week in the PR for their current timetable change.)
