There are lots of places to split. It really depends on the ticket.
For instance on some long-distance trains such as London - Manchester or London - York, there might not be anywhere to split, if the train is running non-stop. (This does not preclude the use of loophole tickets of course.)
A key issue is the distinction between Day and Period.
For longer flows it's typical that returns and singles are valid for more than one day. These tickets are often much more expensive than day singles/returns, and splitting into two or more day singles can save.
Another one is the Network Railcard boundary.
Map is here:
http://www.tfl.gov.uk/assets/downloads/tickets/network-railcard-area.pdf
If you can split at the border (or before), you can potentially use a Network Railcard and save 1/3 off the ticket that is contained within the border. In addition, there will almost always be a Day Single available if you can split.
For example, Bristol - London is £93.50, at peak times for a single. A Day single Bristol - Didcot is £27 and Didcot - London £28.70. So the split saves £££.
Not all trains stop at Didcot, and if they don't, you will be charged.....
Some splits are relevant only at certain times of day, for example, Virgin fares between Rugby and London are ridiculous at peak times, but north from Rugby they don't really bother.
London - Manchester is priced for expense accounts, at £308 return peak, a distance of 184 miles. 82 of these are reaching Rugby, 100 are from Rugby to Manchester.
Yet Rugby - Manchester costs only £46.60 return, at any time.
According to NRE, for tomorrow you can catch a Virgin train to Rugby for only £15 (at 06:03 or 07:03), but that is an Advance ticket. So you could fairly easily do the journey for £76.60 return.
Even on the day, a London Midland Only return from London to Rugby is £69.
Of course this split doesn't fit with the train calling patterns, as there are few trains from Rugby to Manchester direct.
In general for splitting you will look up you fare on brfares.com. If you see it is priced by 'Crosscountry', it's almost certainly overpriced. By checking the stops that your train makes and the train operators running, you can split it into sections priced by other companies and save.
For example, while First Great Western fares between Swindon and Didcot, and Didcot and London are very high (at peak times at least), many of their other fares are very reasonable.
For immediate travel, a Didcot - Birmingham single is £42.50, at any time of day. Brfares shows this to be priced by Crosscountry, hence why it is such an obscene price.
http://www.brfares.com/#!fares?orig=DID&dest=0418
The route is Didcot - Oxford - Banbury - Birmingham.
Didcot - Banbury is primarily operated by First Great Western, and a ticket costs just £8.50 off-peak
http://www.brfares.com/#!fares?orig=DID&dest=BAN
Banbury - Birmingham is then a more reasonable £17
http://www.brfares.com/#!fares?orig=BAN&dest=BHM
Reducing the fare to £25.50
The existence of fare differentials between different operators and on different flows is what creates anomalies. Knowing that fares via Birmingham tend to be priced by Crosscountry and hence expensive but with cheaper fares on either side priced by London Midland, First Great Western, Arriva Trains Wales, and even Virgin, allows us most trivially to deconstruct an expensive journey into sections priced by cheaper TOCs rather than the through fare priced by Crosscountry, or on a more advanced basis to attempt to discover a fare valid over the longer journey that is priced by a different TOC.
