There are several scenarios where breaking up your ticket can be cheaper. The main ones are for journeys at the times of day when the Peak and Off-Peak windows change, and for journeys spread across multiple train operating companies.
Times of day example
If you were taking a train that departed just before the Off-Peak time, you would still need a Peak ticket. But in reality, you may only need a Peak ticket for the first few stops and could use an Off-Peak ticket for the rest of the journey. So, it could be cheaper having two tickets: a Peak one for the first few stops, and an Off-Peak one for all the rest.
Multiple train companies
Journeys with sections covered by different train operating companies can also create pricing anomalies, which we find for you as well.