The SWR delay repay portal requires you to use their search function to state your intended itinerary, which only presents options that respect minimum connection times. Did you enter your full journey from Sheffield to Basingstoke, and if so, when the system offered the 14:37 departure with a 18:15 arrival, did you instead go to "Manually enter your journey" and put in an itinerary fouling the minimum connection time?
Anyway, it seems the facts of the case are:
- Your ticket was valid for an itinerary arriving at 18:15
- You actually arrived at 19:12
Hence, as suggested by Bletchleyite and jfollows, you should select the 14:37-18:15 itinerary and claim for a 30-59 minute delay. Given that the intended itinerary is offered by the automatic system, I don't think there's any need to worry about how the claim is presented (indeed there is no way to present the claim any differently - you just click the appropriate buttons).
Further, just to clarify the implication here:
This was the 17:35, due 18:15 in Basingstoke, ironically cancelled. Actual arrival time was 19:12 by getting an earlier service which was then delayed.
Since your booked train at 17:35 was cancelled, travelling on the earlier train at 17:23 is likely to be unquestionably valid (without needing to delve into the issues of reservability vs non-reservability and contractual rights when a company fails to present their intended restrictions clearly to the consumer).