No. In the example under discussion, the peak fare from London to Lancaster should be the sum of the peak fare from London to Preston and the off-peak fare from Preston to Lancaster. There would then be no advantage from split-ticketing.
And how is the London to Preston fare calculated? Is that the sum of the Euston to South Hampstead fare, plus the South Hampstead to....(you get the idea)
You've only posted one tiny piece of the jigsaw. I'd suggest a new thread for your quite radical proposal and a detailed breakdown of how it would
actually work.
Mischief-making maybe, but I feel the whole situation is akin to going to a restaurant, ordering a set three-course meal, leaving before dessert, and being charged more for eating less.
It's more like being told the 3-course set menu of prawns, steak, and ice cream is £20, but you don't want the dessert.
However the prawns and steak you want, separately, cost a total of £25, so you have to order the set menu and waste the dessert.
Very much so!
Some people will disagree; but I can agree to disagree with them
I did precisely that with Dominos Pizza last week. Potato wedges and garlic bread went in the bin (no actual use to me because they aren't gluten free), and them doing so saved me about £7 over just ordering the two pizzas.
You fraudster!

By admitting you had no intention of eating the products, you are depriving the pizza company of revenue to which they are clearly entitled. You failed to pay the appropriate price for the food which you consumed. You in fact bought a completely different product to the one you consumed. The fact that the product you bought happened to contain a couple of pizzas is merely a coincidence.
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1. Go for a very simple pricing system like a kilometric one and accept that there will be some hefty increases as a result, as well as some heavy overcrowding.
I share your concerns but if anyone actually suggests a kilometric system would work, I suggest they can start by
answering these questions!
2. Go reservations-compulsory and price each train in an airline-like manner, with splitting effectively mandatory - then you don't have to worry about how the fares are structured, just what price you are told on booking. Though this would not necessarily solve the Lancaster issue.
Only possible if we get a high speed network duplicating existing services. Not gonna happen any time soon!
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Repeating the same point does not make London to Preston a divisible subsection of a London to Lancaster journey, any more than you can buy a 2-litre bottle of Coke in the supermarket (London to Lancaster SVS) and walk out with five cans (London to Preston journey). You can on the other hand buy a 6-pack of cans (London to Lancaster SOS) but it's going to cost more if you want to choose that option.
Wrong analogy; you physically
can alight at Preston when undertaking a London to Lancaster journey but you physically can't walk out with cans if you buy bottles. A station call is effectively a divider between one can/bottle and another, as it is an opportunity to alight. If we are going to have analogies, they need to be right.
So the analogy would be that a 2-litre bottle costs a lot more than a deal containing a 2-litre bottle and a can, but you must consume it all without a 'break of drink'. You then chuck away the can, which is a breach of the conditions of sale. You are then guilty of breaching the conditions of sale, but there is nothing the shop owner can
actually do if you've then left the premises. If a shop had such a condition of sale, I would not disagree that a customer who chucks away the can broke it, but you can't deny the fact that they
physically can do so.
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What are the holes you speak of with regards to stopping short but buying a ticket from Lostock Hall to Preston? Unless you're physically caught getting off the train...
Unless a Season or Rover/Ranger etc is part of the equation, the train would need to
call at Lostock Hall. If you are seen alighting from a train that has not called there and/or no train has recently arrived from that station, then if you are unable to present a valid combination, you are going to have problems. Not recommended.
I'll maintain my position that a Lancashire Day Ranger used in conjunction with a Lancaster ticket would be valid though. As would the return portion of a return ticket, of course.