I apologize if I've caused confusion. Like I said my use of the word "splitting" was my clumsy way of describing getting to Chichester without going to London. What James has described is the real and true practice of split ticketing.
https://www.bbc.com/news/uk-51077807
And from Man in Seat 61 website --
==>"Split-ticketing...
Split the journey, where two tickets are cheaper than one...
You'll sometimes find a situation where the cost of a ticket from A to B plus a ticket from B to C is less than the cost of a ticket from A to C. As long as the train stops at 'B', you're legally entitled to use a combination of tickets, there is no need to get off the train. Check your journey at www.trainsplit.com.
Such situations arise in two ways: First, where different pricing managers from different train companies price the various sections of route, and have not noticed the anomaly, and second, where part of the journey can be made with an Off-Peak fare even if the other part has to be done on a peak Anytime fare, which saves money over making the whole trip with a peak Anytime ticket. Anomalies are less likely to happen on obvious direct routes to and from London, as these will usually be priced by one pricing manager working for one train company who will naturally avoid creating them if he can.
For example, rather than buy a Penzance to Birmingham Off-Peak ticket you can save money by buying a Penzance to Cheltenham Off-peak ticket plus a Cheltenham to Birmingham Off-peak ticket, as all the Penzance-Birmingham trains call at Cheltenham. Under Condition 19 of the National Rail Conditions of Carriage there is no need to get off the train, as long as the train itself stops there.
How to check if split-ticketing will save you money:
Go to www.trainsplit.com and use their journey planner. You then click to buy all the tickets online as one transaction, as easily as buying one ticket. There's no booking fee unless they make you a saving, then they take a small fee out of the saving.
The benefit (if any) of split ticketing varies enormously from route to route and time period to time period. I might only save 60p on an off-peak 45-mile trip from Aylesbury to London, but if I needed to catch the 07:06 from London to Plymouth tomorrow morning I could save almost £40 using these systems."
The Man in Seat 61 says... "I have put www.trainsplit.com through its paces and have been surprised at the savings it finds on many routes when booking longer-distance off-peak & anytime fares. I checked these claims using nationalrail.co.uk, and they were correct! I'm not sure I'd now buy any long-distance flexible ticket without at least checking it.
Split the journey, to avoid paying peak fares for the whole trip...
You can sometimes save money by splitting the journey into two tickets if your chosen train starts as a peak train but becomes an off-peak train en route. This often happens where Off-peak fares carry an 'any departure after 09:30' restriction, as they do in much of the Greater London area. For example, if you need a train leaving at 09:15 and arriving 10:00, why pay the peak 'Anytime' rate for your whole journey, it might be cheaper to pay the peak 'Anytime' rate to the first station at which the train stops after 09:30, then pay the cheaper Off-Peak rate from that station onwards. The split-ticketing system at www.trainsplit.com can also check to see if this will save you money."<==