Sorry to jump back a few posts, but . . . .
If they are on the train which is the first booked train on the second ticket, they have not missed it, have they? Infact you could argue that they arrived at the station in good time to catch it, as clearly they did, or atleast, as far as the contract is concerned they did. I think this is a slightly different scenario.
There would be another very relevant significance to this interpretation, if it was to be applied to passengers delayed by their earlier services:
Passengers are aware that sometimes TOCs vary their operational schedules in response to disruption and, consequently, become unsure about their oneard travel. Lets look more closely at what is meant by 'arrived at the station in good time' when in fact they were travelling on a seriously delayed servce:
This interpretation suggests that 'in good time' is NOT a predictable and absolute condition which any reasonable person could be expected to take responsibility for.
An analysis of 'in good time' as you have presented it, HHF, would define it as a
post hoc condition which, after the event, can be seen to have either been fulfilled or not.
The TOC may simply delay the subsequent service (long distance operators usually have no alternatve), or may substitute another train-set to meet the timetabled committments and abandoning the earlier stops of the full service.
We'd have to contrast that retrospective analysis with the
a priori condition which any reasonable person could be expected to have been able to anticipate WITHOUT knowing how events would ultimately transpire on the day of travel. That would be that there MIGHT be delays; it is not reasonable that a passenger could anticipate how a TOC manages the disruptions (by delaying subsequent calling patterns on the same service(s) as you've suggested, or by providing alternative means).
Its technically possible that the passenger travellng KGX-LDS finds that their tickets become technically 'invalid' when arriving at Doncaster after having been delayed at Grantham. Even if they intended travelling on the same train from St.P to Leeds and had tickets authorising this (see yesterday's posts for route details).
Can we therefore, please look again at the situation of the passenger holding two consecutive Advance tickets who, without any possibility of prior knowledge, finds that the TOC who conveys them decides to respond to disruption by running a scheduled service ahead on time, and consequently leaves the delayed passenger at the linking-point between the two tickets. All of this being decided and implemented without any dialogue with the other party to 'the contract'? The passenger?