Personally, although I can see that the could be some advantages to changing ticket prices (especially the likes of LM who have very busy trains filled with lots of people, quite a few of whom would be traveling anyway, using very cheap advanced tickets), the way to "reduce" the costs of railways by increasing passenger numbers is to increase the profitability of NR by running services on lines that are running relatively few services.
For instance the double track lines that only have 2tph in each direction or less, then those lines could be looked at to see if there was a way to increase frequencies along the line. Note that may mean that to justify the increase in frequency that two different under used lines are linked to improve the attractiveness of rail. Some lines may not currently be linked, but even those that currently just require a change should be looked at.
The reason for doing so is that the cost of checking and maintaining lines are broadly similar with 1tph or 6tph, yet if you increase the number coaches that run over a line from 8 per hour to 12 per hour then the income to NR (assuming the same class of unit) would go up by 50%.
In the short term the cost of the extra rolling would be more, but if done carefully it could become cost neutral to the TOC relatively quickly.
Given where it is it wouldn't be likely to be practical, however travel from my home to work takes 45 on the train, but can take up to 75 minutes, but at least 60 minutes station to station because of the change time. That sort of reduction, especially as off peak it takes about 40 minutes to drive, could mean that more people would consider to take the train.
Yes it wouldn't ease congestion on trains into London, it could spread the load, so that getting on and off of trains was faster as those going between local stations could switch to the new service and not congesting the London bound trains.
The problem is to run an extra train service where it takes just under an hour requires a further two units, meaning on electrified lines that generally means a 4 coach train that it would require a lot of people (circa 500 to 1000 per day, assuming an average fare of £5-£10).